# geometry

the lenght of a rectangleis 6 inches more than its width. The area of the rectangle is 91 square inches. Find the dimensions of the rectangle

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1. length is 13 inches
width is 7 inches
let width and length both be x;
(x+6) [this is length] & (x) [this is width];
(x+6) * x = 91;
x^2+6x = 91;
x^2 + 6x - 91 = 0;
solve by factoring;
(x-7)(x+13)= 0
x = 7 & x = -13 (-13 is not real)
check;
L=(7+6)
W= 7
(7+6)*7=91

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2. Width = W.
Length = W+6.

A = L*W = (W+6)W = W^2+6W = 91.
W^2+6W-91 = 0. -91 = -7*13. sum = -7+13 = 6 = B.
(W-7)(W+13) = 0
W = 7 and -13.
w = 7 in.
L = W+6 = 7+6 = 13 in.

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