Question

Find the area of a rectangle plot one side of which is 48 m and its diagonal 50m.

Answer 1

Heya!!!

Area of rectangle = Length × Width

_______________________________

Length = 48m Widht = ?

Let the width be = dm

USING PYTHAGORAS THEOREM!

( 50 )² = ( 48 )² + d²

=>

d =√( 2500 - 2304 )

=>

d = 14m or d = -14m

=>

d = -14m Will be rejected ( y? )

So, d = 14m

So, The area of rectangular plot is

= 14m × 48m = 672m²

Answer 2

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

$\text{The area of the Rectangle = 672 sq.m}$

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

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

One side of the Rectangle = 48 m

Diagonal = 50 m

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

The area of Rectangle

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

Refer the Attachment for the diagram.

We can find the another side by Pythagoras theorum

In ∆ ACD,

→ Hypotenuse = AD = 50 m

→ Base = CD = 48 m

→ Height = AC = x m

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

$\tt{\implies {(50)}^{2} = {(48)}^{2} + {(x)}^{2}}$

$\tt{\implies2500 = 2304 + {x}^{2} }$

$\tt{\implies {x}^{2} = 2500 - 2304 }$

$\tt{\implies {x}^{2} = \sqrt{196} }$

$\begin{array}{r|l}2 & 196 \\\cline{1-2} 2& 98 \\\cline{1-2} 7 & 49 \\ \cline{1-2} 7 & 7 \\\cline{1-2} & 1\end{array}$

196 = 2 × 2 × 7 × 7

Make pairs of common numbers and take only one from them.

$\tt{\Rightarrow7 \times 2}$

$\tt{\Rightarrow14}$

$\tt{\implies {x} = 14}$

${\boxed{\bigstar{\sf\:{Another \: side = 14 \: m}}}}$

As we got the both sides (Length and Breadth) we can find the area.

$\star$ Area of Rectangle =

$\tt{\implies \: length \times breadth}$

$\tt{\implies14 \times 48}$

$\tt{\implies672}$

${\boxed{\bigstar{\sf\:{Area = {672 \: m}^{2} }}}}$

$\therefore$$\text{The area of the Rectangle = 672 sq.m}$