The area of a right-angled triangle is 54 sq. cm. One of its legs has length 12 cm. Find its perimeter. Class 9
R
RBSEGuide
The area of a right-angled triangle is 54 sq. cm. One of its legs has length 12 cm. Find its perimeter. Class 9
Question 1.
The area of a right-angled triangle is 54 sq. cm. One of its legs has length 12 cm. Find its perimeter. Class 9
Solution:
Area of right angled triangle = 54 sq.cm
length of one leg = 12cm
Let h be the length of other leg of right-angled triangle
∵ Area of right-angled triangle
= $\frac{1}{2}$ x product of length of sides containing right angle.
∴ 54 = $\frac{1}{2}$ x 12 x h
∴ 54 = 6h
∴ h = 9 cm
Using Baudhayana-Pythagoras theorem
∵ Hypotenuse² = (one side)² + (other side)²
= 12² + 9²
= 144 + 81
= 225
∴ Hypotenuse = $\sqrt{225}$ = 15 cm
∵ Perimeter of triangle = sum of all sides
= 12 + 9 + 15 = 36
∴ Perimeter of right angled triangle = 36 cm.