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 cm^2, find the dimensions of each square.
2007-05-23 09:11:16 · 2 answers · asked by lo 1 in Science & Mathematics ➔ Mathematics
x^2 + (x + 2)^2 = 100
x^2 + x^2 + 4x + 4 -100 = 0
2x^2 + 4x -96 = 0
x^2 + 2x - 48 = 0
(x + 8)(x - 6)
Obviously x can't equal -8, so x = 6.
You have two squares, one with side 6 and one with side 8, and their areas are 36 and 64.
2007-05-23 09:17:36 · answer #1 · answered by TychaBrahe 7 · 0⤊ 0⤋
Hello
So the first square has an area of x^2 and the second square has an area of (x+2)^2 = x^2 + 4x + 4.
Thus we get x^2 + x^2 + 4x + 4 = 100 = 2x^2+4x-96 = 0
Factor out:
2(x^2+2x-48) ------ 2(x-8)(x+6) = 0
The dimensions are 8x8 and 6x6.
Have a great day
2007-05-23 16:17:47 · answer #2 · answered by Jeff U 4 · 0⤊ 0⤋