Triangle A has a height of 2.5\text{ cm}2.5 cm2, point, 5, start text, space, c, m, end text and a base of 1.6\text{ cm}1.6 cm1, point, 6, start text, space, c, m, end text. The height and base of triangle B are proportional to the height and base of triangle A.
Which of the following could be the height and base of triangle B?
Choose 3 answers:
Choose 3 answers:

(Choice A)
A
Height: 2.75\text{ cm}2.75 cm2, point, 75, start text, space, c, m, end text
Base: 1.76\text{ cm}1.76 cm1, point, 76, start text, space, c, m, end text

(Choice B)
B
Height: 9.25\text{ cm}9.25 cm9, point, 25, start text, space, c, m, end text
Base: 9.16\text{ cm}9.16 cm9, point, 16, start text, space, c, m, end text

(Choice C)
C
Height: 3.2\text{ cm}3.2 cm3, point, 2, start text, space, c, m, end text
Base: 5\text{ cm}5 cm5, start text, space, c, m, end text

(Choice D)
D
Height: 1.25\text{ cm}1.25 cm1, point, 25, start text, space, c, m, end text
Base: 0.8\text{ cm}0.8 cm0, point, 8, start text, space, c, m, end text

(Choice E)
E
Height: 2\text{ cm}2 cm2, start text, space, c, m, end text
Base: 1.28\text{ cm}1.28 cm

Option A

Option D

Option E

Step-by-step explanation:

we know that

If the height and base of triangle B are proportional to the height and base of triangle A

then

Triangle A and Triangle B are similar

Remember that

If two triangles are similar then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

where

h_A and h_B are the height of triangle A and triangle B

b_A and b_B are the base of triangle A and triangle B

In his problem we have

substitute

Rewrite

Verify all the options

A) we have

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

B) we have

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

The ratios are not equal

That means that are not proportional

therefore

These values could not be the height and base of triangle B

C) we have

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

The ratios are not the same

That means that are not proportional

therefore

These values could not be the height and base of triangle B

D) we have

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

E) we have

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B