# 9.4 Use properties of rectangles, triangles, and trapezoids  (Page 6/17)

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Find the area of a triangle with base $13$ inches and height $2$ inches.

13 sq. in.

Find the area of a triangle with base $14$ inches and height $7$ inches.

49 sq. in.

The perimeter of a triangular garden is $24$ feet. The lengths of two sides are $4$ feet and $9$ feet. How long is the third side?

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. length of the third side of a triangle Step 3. Name. Choose a variable to represent it. Let c = the third side Step 4. Translate. Write the appropriate formula. Substitute in the given information. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question. The third side is 11 feet long.

The perimeter of a triangular garden is $24$ feet. The lengths of two sides are $18$ feet and $22$ feet. How long is the third side?

8 ft

The lengths of two sides of a triangular window are $7$ feet and $5$ feet. The perimeter is $18$ feet. How long is the third side?

6 ft

The area of a triangular church window is $90$ square meters. The base of the window is $15$ meters. What is the window’s height?

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. height of a triangle Step 3. Name. Choose a variable to represent it. Let h = the height Step 4. Translate. Write the appropriate formula. Substitute in the given information. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question. The height of the triangle is 12 meters.

The area of a triangular painting is $126$ square inches. The base is $18$ inches. What is the height?

14 in.

A triangular tent door has an area of $15$ square feet. The height is $5$ feet. What is the base?

6 ft

## Isosceles and equilateral triangles

Besides the right triangle, some other triangles have special names. A triangle with two sides of equal length is called an isosceles triangle    . A triangle that has three sides of equal length is called an equilateral triangle    . [link] shows both types of triangles. In an isosceles triangle, two sides have the same length, and the third side is the base. In an equilateral triangle, all three sides have the same length.

## Isosceles and equilateral triangles

An isosceles triangle has two sides the same length.

An equilateral triangle has three sides of equal length.

The perimeter of an equilateral triangle is $93$ inches. Find the length of each side.

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Perimeter = 93 in. Step 2. Identify what you are looking for. length of the sides of an equilateral triangle Step 3. Name. Choose a variable to represent it. Let s = length of each side Step 4. Translate. Write the appropriate formula. Substitute. Step 5. Solve the equation. Step 6. Check:  Step 7. Answer the question. Each side is 31 inches.

Find the length of each side of an equilateral triangle with perimeter $39$ inches.

13 in.

Find the length of each side of an equilateral triangle with perimeter $51$ centimeters.

17 cm

Arianna has $156$ inches of beading to use as trim around a scarf. The scarf will be an isosceles triangle with a base of
$60$ inches. How long can she make the two equal sides?

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. P = 156 in. Step 2. Identify what you are looking for. the lengths of the two equal sides Step 3. Name. Choose a variable to represent it. Let s = the length of each side Step 4. Translate. Write the appropriate formula. Substitute in the given information. Step 5. Solve the equation. Step 6. Check: Step 7. Answer the question. Arianna can make each of the two equal sides 48 inches long.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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Good
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight? By OpenStax By OpenStax By David Corey By Rachel Woolard By Richley Crapo By OpenStax By Richley Crapo By Anh Dao By Madison Christian By Eddie Unverzagt