The side of the square is (x + 5) cm and the base of the right tangled triangle is (x + 9) cm. The perimeter of the square is 80 cm. If the area of the right angled triangle is 84 cm². Find the height of the right angled triangle.

Given:

Side of the square = (x + 5) cm

Perimeter of the square = 80 cm

Base of the right-angled triangle = (x + 9) cm

Area of the right-angled triangle = 84 cm²

Formula used:

1. Perimeter of the square = 4 × side

2. Area of a right-angled triangle = \(\frac{1}{2} \times \text{base} \times \text{height}\)

Calculations:

From the perimeter of the square:

4 × (x + 5) = 80

⇒ x + 5 = 20

⇒ x = 15

Now, base of the right-angled triangle = (x + 9) = 15 + 9 = 24 cm

Let the height of the right-angled triangle be h cm.

Using the area formula:

\(\frac{1}{2} \times 24 \times h = 84\)

⇒ 12h = 84

⇒ h = \(\frac{84}{12} = 7\) cm

∴ The height of the right-angled triangle is 7 cm.