The length of each side of a square is 3 in. more than the length of each side of a smaller square.

Question

The sum of the areas of the squares is 185 in squared .

Answer 1

The length of each side of a square is 3 inches more than the length of each side of a smaller square.

Let's let the smaller square side be variable X.

 

One side of the larger square is X+3.

 

The sum of the areas of the squares is 185 inches²

 

The area if a square is the square of the sides (x²) for the smaller one and (x+3)² for the larger one.

 

The area of the larger one would be x²+6x+9.  Now we add the smaller square

 

x²+6x+9+x²=185

 

Combine the like terms and you have 2x²+6x+9=185

 

Subtract 9 from both sides you get 2x²+6x=176

 

To write in standard form we need to subtract 176 from both sides so the equation will equal zero.

 

2x²+6x-176=0

 

We can factor out a 2:

 

x²+3x+88=0

 

We can factor and then solve:

 

x²+11x-8x-88=0

 

X(x+11)-8(x+11)=0

(x-8)(x+11)=0

(x-8)=0  or (x+11)=0

 

X=8 or x=-11

 

We can drop the negative number.  So the side of the smaller square is 8 inches and the side of the larger square is 11 inches.

 

Now lets check it:  8*8=64  and 11*11 is 121.  64+121=185. 

Answer 2

s=side of smaller square , s+3 = side of larger square

s²+(s+3)²=185

s²+s²+6s+9=185

2s²+6s-176=0

s²+3s-88=0

(s+11)(s-8)=0

s=-11 not possible or s=8

8²+(8+3)²=64+121=185