Question 607492
A rectangle has a diagonal that measures 10 centimeters and a length that is 2 centimeters longer than the width. What is the width of the rectangle in centimeter? 
.
Let w = width
then
w+2 = length
.
applying Pythagorean theorem:
w^2 + (w+2)^2 = 10^2
w^2 + (w+2)(w+2) = 100
w^2 + w^2+4w+4 = 100
2w^2+4w+4 = 100
2w^2+4w-96 = 0
2w^2+16w-12w-96 = 0
(2w^2+16w)-(12w+96) = 0
2w(w+8)-12(w+8) = 0
(w+8)(2w-12) = 0
w = {-8, 12/2}
w = {-8, 6}
Throw out the negative solution (extraneous) leaving:
w = 6 cm