Question

Find the area of a right angled triangle whose hypotenuse is 25cm ,base is 20cm?

Answer 1

Given ,

Hypotenuse of Δ (h) = 25 cm

Base of Δ (b) = 20 cm

Let , the perpendicular of Δ be " x "

Thus ,

$\Rightarrow \sf {(25)}^{2} = {(x)}^{2} + {(20)}^{2} \: \: \: \: \{ \because Pythagoras \: theorem \} \\ \\\Rightarrow \sf 625 = {(x)}^{2} + 400 \\ \\ \Rightarrow \sf {(x)}^{2} = 225 \\ \\ \Rightarrow \sf x = 15 \: \: cm$

Now , the area of triangle is given by

$\sf \large{ \fbox{Area = \frac{1}{2} \times base \times height }}$

Thus ,

$\Rightarrow \sf Area = \frac{1}{2} \times 20 \times 15 \\ \\ \Rightarrow \sf Area = 10 \times 15 \\ \\ \Rightarrow \sf Area = 150 \: \: {cm}^{2}$

$\therefore \sf \bold{ \underline{The \: area \: is \: 150 \: {cm}^{2} }}$