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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 270 cm2.
Other leg of first triangle = √(132 – 52) = √(169 – 25) = √144 = 12 cm
Area = (1/2) × 5 × 12 = 30 cm2
Second triangle similar with hypotenuse 39 ⇒ Scale factor = 39/13 = 3
Area ratio = (Scale factor)2 = 32 = 9
Area of second triangle = 30 × 9 = 270 cm2