Question

You have two squares. The larger square has a side of 3 more than the smaller square. If the combined area of the two squares is 89 cm squared. What is the length of the smaller square.

A. 3

B. 5

C. 8

D. 10

Answer 1

The length of a side of the larger square is 3 cm more than the length of a side of the smaller square.
let the side of the smaller square is a cm then larger square has sides a+3 cm
The sum of the area of two squares is 89 square centimeters.
so a^2+(a+3)^2=89
or a^2+a^2+9+6a=89
or 2a^2+6a-80=0
or a^2+3a-40=0
or a^2+8a-5a-40=0
or a(a+8)-5(a+8)=0
or (a+8)(a-5)=0
or a+8=0=> a=-8 rejected for -ve value
then (a-5=0 =>a=5 the side of the smaller square
& the sides of the larger square is 3+5=8 cms
ans

Answer 2

The length of the SMALLER square is:
B. 5

Basically I tested each answer choice and see if all the information matches it.
Lets check how my answer is correct:
We know that:
The length of the bigger square is 3 more than the smaller square’s length.
The areas of both squares add up to 89 cm^2
length of the SMALLER square is: 5 cm
length of the LARGER square:
5 + 3 = 8 cm

Area of smaller square:
5^2 = 25 cm^2

Area of bigger square:
8^2 = 64 cm^2

ADD UP BOTH AREAS OF SQUARES:
25 + 64 = 89 cm^2

Hope this helps!