Question

The following two triangles have the same angles, and are similar. What is the ratio of height to base for the triangles?

A) .75
B) 1.00
C) 1.25
D) 2.50

Answer 1

height to base =  3 : 4  or 0.75

Answer 2

Answer: The correct option is (A) 0.75.

Explanation: Given that the two right-angled triangles in the figure are similar. We are to find the ratio of the height to the base for the triangles.

In the first triangle,

height, h = 6 units and base, b = 8 units,

In the second triangles,

height, h' = 3 units and base, b' = 4 units.

Since the two triangles are similar, so the corresponding sides will be proportional.

We can see that

`(h)/(h')=(b)/(b')=(6)/(8)=(3)/(4)=0.75.`

Hence, we can write

`(h)/(b)=(h')/(b')=0.75`

Therefore, the ratio of the height to the base of the triangles is 0.75.

Thus, (A) is the correct option.