Question

In the figure below, △ A B C ∼△ D E F . BX and EY are altitudes of each triangle. Find the measure of EY to the nearest tenth.

Answer 1

EY≅ 5.33 cm (nearest to tenth)

Explanation:

Two triangles are said to be similar to each other if they have the same shape

(not necessarily the same size) and their corresponding sides are in

proportion

Given that,

AB = 12

DE = 8

BX = 8

ΔABC ∼ ΔDEF means that

1. ∠A ∼= ∠D, ∠B ∼=∠E and ∠C ∼= ∠F.
2. Further more, their corresponding sides are in proportion.

So,

12/8 = 8/EY

(by doing cross multiplication)

12EY = 8 × 8

12EY = 64

EY = 64 / 12

EY= 5.3333

EY≅ 5.33 cm (nearest to tenth)