find length and width of a triangle

The Phillips family wants to fence their backyard. They know the yard has a perimeter of 24 meters and an area of 32 square meters. What is the yard's length and width?

Assuming that the yard is a rectangle

Area = length × width
32 = length × width

Perimeter = 2 × length + 2 × width

24 = 2 × length + 2 × width

Using 32 = length × width, width = 32 / length

Replace width = 32 / length in 24 = 2 × length + 2 × width


We get:

24 = 2 × length + 2 × (32 / length)

24 = 2length + 64 / length

24 - 2length = 64 / length

Multiply both sides by length

24 × length - 2length × length = ( 64 × length ) / length


24length - 2length2 = 64


24length - 24length - 2length2 = 64 - 24length

0 - 2length2 = + 64 - 24length

0 - 2length2 + 2length2 = 64 - 24length + 2length2


0 + 0 + = 64 - 24length + 2length2

2length2 - 24length + 64 = 0

Divide both sides by 2

length2 - 12length + 32 = 0

Look for factors of 32 that will add up to -12

-8 × -4 = 32 and -8 + -4 = -12

So our factors are -8 and -4

We get (length + -8) × (length + -4) = 0

length + -8 = 0

length + -4 = 0


length = 8

length = 4


If length = 8, width = 32 / length = 32 / 8 = 4

If length = 4, width = 32 / length = 32 / 4 = 8


Thus, either the length = 4 and the width = 8 or the length = 8 and the width = 4





Comments for find length and width of a triangle

Average Rating starstarstarstarstar

Click here to add your own comments

Mar 02, 2017
Rating
starstarstarstarstar
A tree of 90 degree height situated on one back of a river makes an angle of 30degree at a point directly on the opposite of the river find the width of the river NEW
by: Anonymous

A tree of 90 degree height situated on one back of a river makes an angle of 30degree at a point directly on the opposite of the river find the width of the river


Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Algebra word problems.







Recent Articles

  1. Comparison Word Problems

    Jul 25, 17 09:06 PM

    Learn to solve comparison word problems using modeling

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Page copy protected against web site content infringement by Copyscape








Recent Lessons

  1. Comparison Word Problems

    Jul 25, 17 09:06 PM

    Learn to solve comparison word problems using modeling

    Read More