MAT 110 College Algebra

Sec. 1.5

Exercise 17

 

The length of each side of a square is 3 in. more than the length of each side of a small square the sum of the areas of the squares is 149 in.2  Find the lengths of the sides of the two squares.

 

SOLUTION:

Small square has sides x

Larger square has sides (x + 3)

Small square has area x2

Larger square has area (x + 3)2

Sum of the areas is:              x2 + (x + 3)2

 

Equation is:                          x2 + (x + 3)2 = 149

 

Solve:                                  x2 + (x2 + 6x + 9) = 149

                                  2x2 + 6x + 9 – 149 = 0

                                  2x2 + 6x – 140 = 0

                                  x2 + 3x – 70 = 0

                                  (x + 10) (x – 7) = 0

 

                                           x = 7

 

So small square has side 7, and larger square has side 7 + 3 = 10

 

CHECK: areas 7x7 = 49 and 10x10 = 100 for combined areas of 49 + 100 = 149, checks.