Question

find the area of a rectangular plot one side of which measure 70 m and the diagonals is 74m.

Answer 1

Let ABCD be rectangle
Where,AB=DC=length
BC=AD=breadth=70m
AC=diagonal=74m
In triangle ABC,
BY PYTHAGORAS THEORUM
AB²+BC²=AC²
AB²=AC²-BC²
=(74)²-(70)²
= 5476-4900
= 576
=√576
AB = 24
Area of rectangle
= Length * Breadth
= 24 * 70
= 1680m²

Answer 2

∴ Area of Rectangle plot is $1680m^{2}$

Step-by-step explanation:

Given;

A Rectangular plot,which one side is $70m$ and diagonals is $74m$

∵ In a Rectangle all angle are $90degree$

From figure;

$AB^{2} +BC^{2}=AC^{2}$

⇒$BC^{2}=AC^{2}-AB^{2}$

Plug the values;

⇒$BC^{2}=74^{2}-70^{2}$

⇒$BC=\sqrt{576}$

∴$BC=24$

∴Area of Rectangle plot is,

  $=AB\times BC$

 $=70\times 24$

 $=1680$$m^{2}$

So Area of Rectangle plot is $1680m^{2}$