A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. A second right-angled triangle is similar to the first, and its hypotenuse is 39 cm. What is the area of the second triangle?

Correct option is D

Given:
First right-angled triangle:
Hypotenuse = 13 cm
One leg = 5 cm
Second right-angled triangle is similar to the first.
Hypotenuse of second triangle = 39 cm
Formula Used:
Pythagoras theorem: Hypotenuse² = Base² + Height²
Ratio of areas of similar triangles = (Ratio of corresponding sides)²
Solution:
13² = 5² + x²
169 = 25 + x²
x² = 144 => x = 12 cm
Area of the first triangle = $$\frac 12$$​ × 5 × 12 = 30 cm²
Scale factor =$$\frac {39}{ 13}$$​ = 3
Area of the second triangle = 30 × 3² = 30 × 9 = 270 cm²
Therefore, the area of the second triangle is 270 cm².