Question

A rectangular garden will be divided into two plots by fencing it on the diagonal. The diagonal distance from one corner of the garden to the opposite corner is five yards longer than the width of the garden. The length of the garden is three times the width. Find the length of the diagonal of the garden.

Short answer

Length of diagonal of garden is 6.2 yards.

Step-by-step solution

Step 1. Given Information

Diagonal is w+5 yards and width is w and 3w is length.

Step 2. Formula for rectangular diagonal

On applying the formula of rectangular diagonal,

$$\begin{gathered} {\mathrm{Length}}^2+{\mathrm{width}}^2={\mathrm{diagonal}}^2 \\ 3\mathrm{w}+{\mathrm{w}}^2=\mathrm{w} \\ 9{\mathrm{w}}^2+{\mathrm{w}}^2=\mathrm{w} \\ {\left(\sqrt{10}\mathrm{w}\right)}^2=\mathrm{w}\mathrm{w}+5=\sqrt{10}\mathrm{w} \\ \mathrm{w}-\sqrt{10}\mathrm{w}=-5 \\ \mathrm{w}(1-\sqrt{10})=-5 \\ \mathrm{w}=\frac{-5}{1-\sqrt{10}} \\ \mathrm{w}=\frac{-5}{1-\sqrt{10}} \\ \mathrm{w}=\frac{5}{1+\sqrt{10}} \\ \mathrm{w}\approx 1.20 \end{gathered}$$

The diagonal is 1.2+5=6.2 yards