Question

Consider a right angle triangle where the length of the shorter leg is one third of the length of its hypotenuse. If the length of the shorter leg is 7 cm, then calculate the area of thetriangle in square cm.

Answer 1

Hope it helps you makE sure you do the prime factorisation correct

Answer 2

Answer:

The area of the triangle is 69.293 sq.cm.

Step-by-step explanation:

Length of shorter leg = 7 cm

We are given that the length of the shorter leg is one third of the length of its hypotenuse.

$7 = \frac{1}{3} Hypotenuse$

Hypotenuse = 21 cm

One leg of right angle = 7 cm

We will use Pythagoras theorem

$Hypotenuse^2=Perpendicular^2+Base^2$

$21^2=7^2+Base^2$

$\sqrt{21^2-7^2}=Base$

$19.798=Base$

Area of triangle = $\frac{1}{2} \times Base \times Height$

Area of triangle = $\frac{1}{2} \times 7 \times 19.798$

Area of triangle = $69.293 cm^2$

Hence The area of the triangle is 69.293 sq.cm.