Question

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

Answer 1

We know that all the angles of a rectangle are 90° and the diagonal divides the rectangle into two right angled triangles.
So, 48 m will be one side of the triangle and the diagonal, which is 50 m, will be the hypotenuse.
According to the Pythagoras theorem:
(Hypotenuse)² = (Base)² + (Perpendicular)²
Perpendicular = $\sqrt{{\left(\mathrm{Hypotenuse}\right)}^2-(\mathrm{Base}{)}^2}$
Perpendicular = $\sqrt{{\left(50\right)}^2-{\left(48\right)}^2}=\sqrt{2500-2304}=\sqrt{196}=14$ m
∴ Other side of the rectangular plot = 14 m
Length = 48m
Breadth = 14m

∴ Area of the rectangular plot = 48 m $\times$ 14 m = 672 m²
Hence, the area of a rectangular plot is 672 m².