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
Aug 09, 16 01:40 PM
Average age of Dipu and Apu is 22 years. Average age of Dipu and Tipu is 24 years. Age of Dipu is 21 years. What are the ages of Apu, and tipu ? Let
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