Question
Find the area of a rectangular plot on side of which is $48m$ and its diagonal $50m.$
✓
Answer
We know that all the angles of a rectangle are $90^{\circ}$ and the diagonal divides the rectangle into two right angled triangles.
So, one side of the triangle will be $48 m$ and the diagonal, which is $50 m$ , will be the hypotenuse.
According to Pythagoras theorem:
$(\text { Hypotenuse })^2=(\text { Base })^2+(\text { Perpendicular })^2$
Perpendicular $=\sqrt{(\text { Hypotenuse })^2-(\text { Base })^2}$
Perpendicular $=\sqrt{(50)^2-(48)^2}$
$\therefore$ Other side of the rectangular plot $=14 \mathrm{~m}$
$\therefore$ Area of the rectangular plot $=48 \mathrm{~m} \times 14 \mathrm{~m}=672 \mathrm{~m}^2$
Hence, the area of a rectangular plot is $672 \mathrm{~m}^2$.
So, one side of the triangle will be $48 m$ and the diagonal, which is $50 m$ , will be the hypotenuse.
According to Pythagoras theorem:
$(\text { Hypotenuse })^2=(\text { Base })^2+(\text { Perpendicular })^2$
Perpendicular $=\sqrt{(\text { Hypotenuse })^2-(\text { Base })^2}$
Perpendicular $=\sqrt{(50)^2-(48)^2}$
$\therefore$ Other side of the rectangular plot $=14 \mathrm{~m}$
$\therefore$ Area of the rectangular plot $=48 \mathrm{~m} \times 14 \mathrm{~m}=672 \mathrm{~m}^2$
Hence, the area of a rectangular plot is $672 \mathrm{~m}^2$.
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