Question

Find the area of rectangular plot, one side of which is 45 m and diagonal is 50 m.​

Answer 1

Answer:

$\red\bigstar$ Area of the rectangle = 981 m².

SOLUTION

Let us assume that 45 m is the length of the rectangle.

Diagonal of the rectangle = 50m.

Now,

Let us consider a rectangle ABCD ,where AC is  the diagonal .

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large 45m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 50m}\end{picture}$

Now let us find the breadth of rectangle ABCD.

$\implies$ (Diagonal)² - (Length)² = (Breadth)²

$\implies$   AC² - AB² = BC²

$\implies$ 50² - 45² = BC²

$\implies$ 2500 - 2025 = BC²

$\implies$ 475  = BC²

$\implies$ BC = √475

$\implies$ Breadth (b) of the rectangle = 21.7944 ≈ 21.8cm.

AREA

Area of a rectangle = l × b , Where l is the length and b is the breadth of rectangle.

Here,

l = 45m.

b = 21.8

$\implies$ Area of the rectangle = 45 × 21.8

$\implies \tt Area \: of \:the\: rectangle = 981 m^2$

Answer 2

Given

• One side of rectangular plot = 45 m
• Diagonal length = 50 m

To find

• Area of rectangular plot

Solution

We have a side of a rectangular plot, and diagonal length, we shall find the area, for finding area we need the another side.

Let us consider the given side 45 m as length and other side be breadth, and we have diagonal, using pythagoras theorem, let's find breadth.

• Breadth² = Diagonal² + Length²
• Breadth² = 50² - 45²
• Breadth² = 2500 - 2025
• Breadth² = 475
• Breadth = √475
• Breadth = 21.8  

Hence, the breadth of the rectangular plot is 21.8 m

Now, we have length and breadth, let's find the area :-

• Area = Length × Breadth
• Area = 45 × 21.8
• Area = 981

Hence, the area of the rectangular plot is 981 m²