Question

Find the perimeter of a rectangle if on of its sides is 24cm and diagnol is 25cm

Answer 1

$\textbf{\large{\underline{Answer :-}}}$

$\text{The Perimeter of Rectangle is 62 cm}$

$\textbf{\large{\underline{Explanation :-}}}$

Given :

Measure of one side = 24 cm

Diagonal's Measure = 25 cm

To find :

The Perimeter of Rectangle

Solution :

To get the Perimeter, we need to find the measure of the second side.

Using Pythagoras Theorem we can find the other side.

Refer the Attachment for better understanding.

By Pythagoras Theorem :

→ Hypotenuse = AD = 25 cm

→ Base = CD = 24 cm

→ Height = AC = x cm

$\star$ (Hypotenuse)² = (Base)² + (Height)²

$\sf{\implies( {25})^{2} = ( {24})^{2} + ( {x})^{2}}$

$\sf{\implies625 = 576 + {x}^{2} }$

$\sf{\implies {x}^{2} = 625 - 576}$

$\sf{\implies {x}^{2} = 49}$

$\sf{\implies \: x = \sqrt{49}}$

Square root of 49 =

$\begin{array}{r|l}7 & 49 \\\cline{1-2} 7 & 7 \\\cline{1-2} & 1\end{array}$

49 = 7 × 7

Square root = 7

$\sf{\implies \: x = 7}$

${\boxed{\bigstar{\sf\:{Breadth \: = 7 \: cm}}}}$

As we got the measurements of the Length and Breadth, we can now find the Perimeter.

$\star$ Perimeter of Rectangle =

${\boxed{\sf\:{Perimeter = 2(Length + Breadth)}}}$

$\sf{\implies2(24 + 7)}$

$\sf{\implies48 + 14}$

$\sf{\implies62}$

${\boxed{\bigstar{\sf\:{Perimeter\: = 62 \: cm}}}}$

$\therefore$$\text{The Perimeter of Rectangle is 62 cm}$

Answer 2

The answer is in the picture