Question

The perimeter of the rectangle whose length is $60cm$and a diagonal is $61cm$ is

• A. $120cm$
• B. $122cm$
• C. $71cm$
• D. $142cm$

Answer 1

The correct option is D

$142cm$

Step 1: Find the length of other side.

Consider, PQRS is a rectangle and triangle PSR is a right angled triangle .

In right angled triangle PSR, using Pythagoras theorem ,

i.e., square of the hypotenuse is equal to the sum of the square of the other two sides.

$$\begin{gathered} \Rightarrow {\left(\mathrm{PR}\right)}^2={\left(\mathrm{PS}\right)}^2+{\left(\mathrm{PR}\right)}^2 \\ \Rightarrow {\left(61\right)}^2={\left(\mathrm{PS}\right)}^2+{\left(60\right)}^2 \\ \Rightarrow 3721={\left(\mathrm{PS}\right)}^2+3600 \\ \Rightarrow {\left(\mathrm{PS}\right)}^2=3721-3600 \\ \Rightarrow {\left(\mathrm{PS}\right)}^2=121 \\ \Rightarrow \mathrm{PS}=\sqrt{121} \\ \Rightarrow \mathrm{PS}=11\mathrm{cm} \end{gathered}$$

Step 2: Find the perimeter of the rectangle.

Perimeter of rectangle PQRS $=2(\mathrm{length}\times \mathrm{breadth})$

$=2(\mathrm{PS}+\mathrm{RS})$

$$\begin{gathered} =2\left(60+11\right) \\ =2\times 71 \\ =142\mathrm{cm}. \end{gathered}$$

Hence, correct answer is (D).