Math Question #1

Question

The length of a rectangle is 1 inch more than its width.The area of the rectangle is 72 square inches. Find the dimensions of the rectangle.

Answer 1

Area= l*w. There are two equations and two unknowns.

72=l*w

l=w+1 substitute the 2nd equation into the first one.

72= w(w+1) distribute

72=w^2 +w subtract 72 from both sides to set it equal to zero.

w^2+w-72=0 factor

(w+9)(w-8)=0

w+9=0 subtract 9 from each side

w+9-9=0-9

w=-9 The width can’t be negative, so this is not the solution. It is extraneous.

w-8=0 add 8 to both sides

w-8+8=0+8

w=8. The width is 8 inches. Substitute this in the equation to get the length. Length=w+1. The length is 8+1=9. The length is 9 inches.

The answer is that the width is 8 inches and the length is 9 inches.