Question

The length of a rectangle is 7 meters more than four times its width if the area of the rectangle is 650 square meters, find the length and the width. round to nearest tenth

Answer 1

Let the width be x.
Width = x
Length = 4x + 7

The area is 650 m²

x(4x + 7) = 650
4x² + 7x - 650 = 0

Using quadratic formula:
$x = \dfrac{-b \pm \sqrt{b^2 - 4ac} }{2a}$

a = 4, b = 7, c = -650

$x = \dfrac{-7 \pm \sqrt{7^2 - 4(4)(-650} }{2(4)}$

$x = 11.9 \ or\ x = -13.7 \text {(rejected, length cannot be negative)}$

Width = 11.9m
Length = 4(11.9) + 7 = 54.6m

Answer: Length = 54.6m and width = 11.9m