Question

A rectangle is 6yards longer than it is wide. Find the dimensions of the rectangle if it’s area is 187 square yards

Answer 1

Answer:

Width = 11 yards

Length = 17 yards

Step-by-step explanation:

First of all, the length of the rectangle is 6 yards longer than the width, this means, length = width + 6 yards. This dimensions can be represented on figure 1, where w is width, and l, for length.

We know the area of a rectangle is A = width x length

For our case 187 = w . (w + 6)

Using the Distributive Property for the multiplication we obtain

$187 = w^{2} +6w$

$w^{2} +6w-187 =0,$

Using the quadratic formula $w=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}$ where a = 1, b = 6, c = - 187 and replacing into the formula, we will have:

$w=\frac{-6\±\sqrt{6^2-4(1)(-187)} }{2(1)}$

$w=\frac{-6\±\sqrt{36+748} }{2}=\frac{-6\±\sqrt{784} }{2}=\frac{-6\±28}{2}$

We have two options: $w=\frac{-6+28}{2}=\frac{22}{2}=11 yards$

Or

$w=\frac{-6-28}{2}=\frac{-34}{2}=-17 yards$ But a distance (width) can not be negative so, this answer for w must be discarded.

The answer must be width = 11 yards.

To find the length $l =\frac{187}{11}=17 yards$