Question

A rectangular lawn has area 140 square yards. Its width that is six less than twice the length. What are the length and width of the lawn?

Short answer

Length and width are 10 and 14 yard respectively.

Step-by-step solution

Step 1. Given Information

Rectangular lawn's area is 140 square yards and width is 6 yard less than twice of rectangle's length.

Step 2. Apply in rectangle area formula

Let's take $\mathrm{x}$be the length and $2\mathrm{x}-6$yard be the width. On applying the data in the rectangle's area formula,

$$\begin{gathered} \mathrm{Length}\times \mathrm{width}=\mathrm{Area} \\ \mathrm{x}(2\mathrm{x}-6)=140 \\ 2{\mathrm{x}}^2-6\mathrm{x}=140 \\ {\mathrm{x}}^2-3\mathrm{x}-70=0 \\ {\mathrm{x}}^2-10\mathrm{x}+7\mathrm{x}-70=0 \\ \mathrm{x}(\mathrm{x}-10)+7(\mathrm{x}-10)=0 \\ \mathrm{x}=10,\mathrm{x}=-7 \end{gathered}$$

The length cannot be negative. So the length will be 10 yards and width is 14 yards.