quadratic applications

Question

The difference of the areas of two squares is 147 square feet. Each side of the larger square is two times the length of a side of the smaller square. Find the length of a side of each square.

Answer 1

A1 - A2 = 147 difference in areas

A1=L1^2 area of A1 is length x width = L1 x L1 = L1^2

A2=L2^2

L1 = 2L2 each side of larger square (L1) is twice that of smaller square (L2)

A1-A2=147

L1^2-L2^2=147

(2L2)^2)-L2^2=147

4L2^2-L2^2=147

3L2^2=147

L2^2=49

L2=7

L1=2L2=2x7=14

 

check: L1^2=14^2=186

L2^2=7^2=49

L1^2-L2^2=186-49 = 147.

Answer 2

Let S = side of smaller square

 

Then 2S = side of larger square

 

The difference of the areas is 147 square feet  ==>  

 

(2S)^2 - S^2 = 147

4S^2 - S^2 = 147

3S^2 = 147

S^2 = 49

S = +7 or -7 

 

Discard the negative answer since the length must be positive

 

So the length of a side of the small square is 7 feet

and the length of a side of the large square is 14 feet 

 

Check :  14^2 - 7^2 = 196 - 49 = 147 square feet