The side of one square is 2 cm longer than the side of a second square.
If the combined area of the squares is 100 square cm, find the dimensions
of each square.
:
The area of the two squares
x^2 + (x+2)^2 = 100
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x + 4 - 100 = 0
2x^2 + 4x - 96 = 0
Simplify, divide by 2
x^2 + 2x - 48 = 0
Factors to
(x+8)(x-6) = 0
the positive solution
x = 6
:
6 by 6 the small square
8 by 8 the large square
;
:
Check: 36 + 64 = 100 Does this make sense to you?
