Question

Use the diagram of two triangles shown below to answer this question.

Triangles ACD and ABE are similar. What is x equal to?

A. 4.8 cm

B. 30.0cm

C. 10.0cm

D. 14.4cm

Answer 1

10.0cm

Explanation:

Answer 2

The answer is C. 10.0 cm.

Explanation:

Since triangles ACD and ABE are similar, the angles within each of them are the same:

This implies that the sine of the angle at A = opposite ÷ hypotenuse (for triangle ACD) = opposite ÷ hypotenuse (for triangle ABE).

Opposite for triangle ACD = 15 cm

Hypotenuse for triangle ACD = 12 + 6 = 18 cm

Opposite for triangle ABE = x

Hypotenuse for triangle ABE = 12 cm

Therefore, 15/18 = x/12

or x = (15 × 12) ÷ 18

x = 10 cm.