The diagram shows three similar right-angled triangles. What is the area of the largest triangle?

Answer:

20) B

Let hypotenuse of smaller triangle = H
Let hypotenuse of larger triangle = A
Let hypotenuse of largest triangle = B

Using Pythagoras theorem, 
H² = 1² + 3²
H² = 1 + 9 = 10
H = √10

Since the triangles are similar,

  3      =     √10 
√10             A

A = (¹⁰⁄₃)

Since larger triangle and largest triangle are similar, 

Small edge of the largest triangle = ⅓ x (¹⁰⁄₆) = (¹⁰⁄₉)

Area of a right angled triangle = ½ x base x height = ½ x (¹⁰⁄₉) x (¹⁰⁄₃) = (¹⁰⁰⁄₅₄) = (⁵⁰⁄₂₇) cm²