Question

The diagonal of a rectangle measures 25cm. The width of the rectangle is 7cm. How do you find the length of the rectangle in cm?

Answer 1

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

The Length of the Rectangle is 24 cm.

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

$\textsf{\underline{\underline{Given :}}}$

The Diagonal measures = 25 cm

The Width = 7 cm

$\textsf{\underline{\underline{To Find :}}}$

The Length of the Rectangle

$\textsf{\underline{\underline{Solution :}}}$

❖ $\textsf{\underline{By Pythagoras theorum :}}$

Refer The Attachment.

⟹ Hypotenuse : 25 cm = AD

⟹ Base : x = CD

⟹ Height : 7 cm = AC

★ (Hypotenuse)² = (Base)² + (Height)²

$\sf{\implies} \: {25}^{2} = {x}^{2} + {7}^{2}$

$\sf{\implies} \: 625 = {x}^{2} + 49$

$\sf{\implies} \: {x}^{2} = 625 - 49$

$\sf{\implies} \: {x}^{2} = 576$

$\sf{\implies} \: x = \sqrt{576}$

$\begin{array}{r|l} 2 & 576 \\\cline{1-2} 2 & 288 \\\cline{1-2} 2 & 144 \\ \cline{1-2} 2 & 72 \\\cline{1-2} 2 & 36 \\\cline{1-2} 2 & 18 \\\cline{1-2} 3 & 9 \\\cline{1-2} 3 & 3 \\\cline{1-2} & 1\end{array}$

⟹ 576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

⟹ 2 × 2 × 2 × 3

⟹ 24

$\sf{\implies} \: x = 24$

${\boxed{\boxed{\sf{x = 24}}}}$

⛬ The Length of the Rectangle is 24 cm.