Question

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

Answer 1

Hint: Here first of all draw the diagram with the help of the given data and find out the required measure to calculate the area of the rectangular plot. Use Pythagoras theorem to find the third side in the right angle. Substitute the values and simplify the equation accordingly.

Complete step-by-step answer:

Let us consider as shown in the above figure ABCD as the rectangular plot.
Given that one side, BC $ = 48m $
AC $ = 50m $
Now, in right angled triangle ABC, $ \angle B = 90^\circ $
By using the Pythagoras theorem which states that in any right angled triangle the square of the hypotenuse is the sum of the square of the adjacent side and the square of the opposite side.
 $ A{C^2} = A{B^2} + B{C^2} $
Place the values in the above equation –
 $ {(50)^2} = A{B^2} + {(48)^2} $
Make the unknown term as the subject –
 $ {(50)^2} - {(48)^2} = A{B^2} $
To simplify the above difference of two squares use $ ({a^2} - {b^2}) = (a - b)(a + b) $
 $
  A{B^2} = (50 - 48)(50 + 48) \\
  A{B^2} = (2)(98) \\
  A{B^2} = 196 \;
  $
Take square root on both the sides of the equation –
 $ \sqrt {A{B^2}} = \sqrt {{{(14)}^2}} $
Square and square-root cancel each other on both the sides of the equation –
 $ \Rightarrow AB = 14m $
Now, the area of the rectangular plot is $ A = l \times b $
Here, length is BC $ = 48m $
And breadth is AB $ = 14m $
Place the values in the formula-
 $ A = 48 \times 14 $
Simplify the above equation –
 $ A = 672{m^2} $
Hence, the required answer – the area of the rectangular plot is $ 672{m^2} $

Note: Remember the properties of the rectangle and its applications accordingly. Remember square and square-roots of the numbers at least till twenty for an accurate and an efficient answer. A rectangle is the quadrilateral. Each interior angle in the rectangle is equal to $ 90^\circ $ and the sum of all the four angles is equal to $ 360^\circ $ . Also, remember that if the diagonals bisect each other at right angles, then the rectangle is called the square.