A plain mat is placed around a picture measuring 28 cm by 36 cm so that the width of the mat is equal on all sides. The area of the mat if 3/4 of the area of the picture. what would the width of the mat be??
2007-11-19 13:39:08 · 2 answers · asked by m 1 in Science & Mathematics ➔ Mathematics
28*36 = (3/4)(2x + 28)(2x + 36)
28*36 = 3(x + 14)(x + 18)
x^2 + 32x + 252 = 312
x^2 + 32x - 60 = 0
(x - 2)(x + 30) = 0
x = 2 cm
2007-11-19 14:11:32 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋
If you let w be the width of the mat, then the area of the picture is 28 * 36 and the area of the mat is (28 + 2w) (36 + 2w) - 28 * 36 (i.e., take the total area minus the area of the picture).
Because the area of the mat is 3/4 times area of picture, you have:
(2w+28) (2w + 36) - 28*36 = (3/4) * 28 * 36
(2w+28) (2w + 36) -(7/4) * 28 * 36 = 0
Simplify by dividing through by 4:
(w+14) (w + 18) - 7 * 7 * 9 = 0
w^2 + 32w - 189 = 0
Using the quadratic formula, I get:
w = (-32 +/- sqrt( 32^2 + 4*189) / 2
It comes out to about 5.095.
2007-11-19 14:09:12 · answer #2 · answered by Dave A 3 · 0⤊ 0⤋