# A rectangle has one side 5 inches and a diagonal of 15 inches. How do you find the perimeter of the rectangle?

Jul 12, 2018

Perimeter of rectangle is $38.28$ inches.

#### Explanation:

Side and diagonal of rectangular is ${s}_{1} = 5 , d = 15$ inches

${d}^{2} = {s}_{1}^{2} + {s}_{2}^{2} \therefore {15}^{2} = {5}^{2} + {s}_{2}^{2}$ or

${s}_{2}^{2} = {15}^{2} - {5}^{2} = 200 \therefore {s}_{2} = \sqrt{200} \approx 14.14$ inches

Perimeter of rectangle is $P = 2 \left({s}_{1} + {s}_{2}\right) = 2 \left(5 + 14.14\right)$

$\therefore P = 2 \cdot 19.14 \approx 38.28$ inches.

Perimeter of rectangle is $38.28$ inches [Ans]