Question

The length of a rectangle is four more than three times its width. the area of the rectangle is 25. write an algebraic model for this situation. solve the equation to find the dimensions of the rectangle.

Answer 1

width (w) = w

Length (L) = 3w + 4

Area (A) = L x w

25 = (3w + 4)w

25 = 3w² + 4w

0 = 3w² + 4w - 25

w = $\frac{-2 +/-\sqrt{79} }{3}$

w ≈ 2.3, w ≈ -3.6 (width cannot be negative!)

w ≈ 2.3

Length (L) = 3w + 4 = 3(2.3) + 4 = 6.9 + 4 = 10.9

Answer: width=2.3, Length=10.9