Math Question #5

Question

The length of a rectangle exceeds its width by 3 inches. The area of the rectangle is 70 square inches. Find the dimensions of the rectangle.

Answer 1

Area =l*w 70=l*w

l=w+3 substitute the 2nd equation into the first.

70= w (w+3)

70=w²+3w set equal to zero by by subtracting 70 from both sides.

w²+3w-70=0 Factor

(w+10)(w-7) =0

w+10=0 subtract 10 from both sides

w+10-10=0-10

w=-10 width cannot be -10. This is an extraneous solution.

w-7=0 add 7 to both sides

w-7+7=0+7

w=7 The width is 7 inches.

substitute this into the formula for length. l=w+3.

l=7+3

The length equals 10 inches.