The length of a rectangle exceeds its width by 2 cm. If its diagonal is 10 cm long, find the width of the rectangle.
+1223 width = x
length = x + 2
Use the Pythagorean Theorem.
\(x^2 + (x+2)^2 = 10^2\)
\(2x^2 + 4x + 4 = 100\)
\(x^2 + 2x + 2 = 50\)
\((x+8)(x-6) = 0\)
Distance can't be negative, so the width is 6 centimeters.
