a rectangle is 3 cm longer and 2 cm narrower than a sqare with the same area. Find the dimensions of each figure.
2007-02-14 16:34:24 · 3 answers · asked by ? 2 in Science & Mathematics ➔ Mathematics
I thank you for helping me out. I think you all deserve points, but since this one only allows me one I will just leave it as is. Thanks!
2007-02-15 12:31:54 · update #1
(x+3)*(x-2)=x^2
solve for x.
2007-02-14 16:39:29 · answer #1 · answered by al 3 · 0⤊ 0⤋
Let x be the width of the square, l the length of the rectangle and w the width of the rectangle.
Since the areas are equal:
x^2 = lw
Also:
l = x + 3
w = x - 2
Substituting:
x^2 = (x+3)(x-2)
=> x^2 = x^2 + 3x - 2x - 6.
=> x = 6
Substiting again:
l = 6 + 3 = 9
w = 6 - 2 = 4
So the square is 6 cm x 6 cm and the rectangle is 9 cm x 4 cm.
2007-02-15 00:42:56 · answer #2 · answered by Groucho Returns 5 · 0⤊ 0⤋
(x+3)(x-2) = x^2
x^2 + x -6 = x^2
x - 6 = 0
x = 6
square is 6 X 6
rectangle is
(x+3) x (x-2)
(6+3) x (6-2)
9 X 4
square is 6 x 6
rectangle is 9 x 4
areas of both are 36
2007-02-15 00:43:40 · answer #3 · answered by Bill F 6 · 0⤊ 0⤋