Question

find the area of a rectangular plot,one side of which is 48m and its diagonal is 50m.​

Answer 1

Answer:

The area is the Rectangle is 672 m².

Step-by-step explanation:

Given :

One side = 48 m

Diagonal = 50 m

To find :

Area of the rectangle

Solution :

Find the measure of the other side by Pythagoras theorem.

Height = y

Base = 48

Hypotenuse = 50

$\boxed{\sf{(Hypotenuse)^{2} = (Base)^{2} + (Height)^{2}}}$

$\sf{\implies} \: {50}^{2} = {48}^{2} + {y}^{2} \\ \\ \sf{\implies} \:2500 = 2304 + {y}^{2} \\ \\ \sf{\implies} \: {y}^{2} = 2500 - 2304 \\ \\ \sf{\implies} \: {y}^{2} = 196 \\ \\ \sf{\implies} \:y = \sqrt{196} \\ \\ \sf{\implies} \:y = 14$

Breadth = 14 m

$\rule{300}{1.5}$

★ Area of the rectangle -

$\boxed{\sf{Area = Length \times Breadth}}$

$\sf{\implies} \: 48 \times 14 \\ \\ \sf{\implies} \: {672 \: m}^{2}$

Area = 672 m²

$\therefore$ The area is the Rectangle is 672 m².

Answer 2

$\huge\underline\mathfrak{Question-}$

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

$\huge\underline\mathfrak{Answer-}$

$\large{\underline{\boxed{\mathrm{Area\:of\:rectangle=672\:m^2}}}}$

$\huge\underline\mathfrak{Solution-}$

We know that,

Diagonal of rectangle = $\bold{\sf{\sqrt{L^2+B^2}}}$

Putting the given values,

: $\implies$ 50 = $\sf{\sqrt{(48)^2+B^2}}$

: $\implies$ (50)² = $\sf{2304+B^2}$

: $\implies$ 2500 - 2304 = B²

: $\implies$ B² = 196

: $\implies$ B = √196

: $\implies$ B = 14 m.

$\therefore$ Breadth of rectangle = 14 m

$\rule{200}2$

Now,

Area of rectangle = Length × Breadth

Putting the values,

: $\implies$ Area of rectangle = 48 × 14

: $\implies$ Area of rectangle = 672 m²

$\large{\underline{\boxed{\mathrm{\therefore\:Area\:of\:rectangle=672\:m^2}}}}$