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  2length^{2} = 64
24length  24length  2length^{2} = 64  24length
0  2length^{2} = + 64  24length
0  2length^{2} + 2length^{2} = 64  24length + 2length^{2}
0 + 0 + = 64  24length + 2length^{2}
2length^{2}  24length + 64 = 0
Divide both sides by 2
length^{2}  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




Jan 15, 18 11:55 AM
Learn how to solve radical equations with rational exponents and those with square roots
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Jan 15, 18 11:55 AM
Learn how to solve radical equations with rational exponents and those with square roots
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.