Question

if the perimeter of a rectangular plot is 68 M and length of its diagonal is 26 m find its area

Answer 1

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Answer 2

Rectangular plot area is $\bold{240 \mathrm{cm}^{2}}$

Solution:

Breadth and Length of the rectangle be l and b respectively.

Given: Perimeter = 68,  

           Length of diagonal, AC = 26

Perimeter of rectangle= 2(l + b) = 68

$l+b=\frac{68}{2}=34$___________ (1)

And by Pythagoras theorem

$\begin{array}{l}{A C^{2}=A B^{2}+B C^{2}} \\ \\{(26)^{2}=l^{2}+b^{2}}\end{array}$

$l^{2}+b^{2}=676$

From (1) equation, l + b = 34  

Squaring on both sides

$\begin{array}{l}{(l+b)^{2}=(34)^{2}} \\ \\{l^{2}+b^{2}+2 l b=1156}\end{array}$

676 + 2 lb= 1156

2 lb = 480

lb= 240

Area = lb = $\bold{240 \mathrm{cm}^{2}}$