Question

Triangle A has a height of 2.5 cm and a base of 1.6 cm. 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? (A) Height: 2.75 cm Base: 1.76 cm (B) Height: 9.25 cm Base: 9.16 cm (C) Height: 3.2 cm Base: 5 cm (D) Height: 1.25 cm Base: 0.8 cmE) Height: 2 cmBase: 1.28 cm

Answer 1

We have that triangle A has

h = 2.5 cm

b = 1.6 cm

The ratio between its height and base is:

hA / bA = 2.5 cm / 1.6 cm

To be proportional to triangle A, triangle B must have the same ration between height and base:

hB / bB = hA / bA = 2.5 cm /1.6 cm

If we see the options, when hB = 1.25 and bB = 0.8, this is the same ratio as

hA / bA, since hB = (hA / 2), and bB = ( bB = bA / 2) or

hB = (2.5/2) = 1.25

bB = (1.6/2) = 0.8

Therefore, we have:

hA / bA = hB / bB = 2.5 cm /1.6 cm = 1.25 cm / 0.8 cm = 1.5625

Thus, the height and the base of triangle B is h = 1.25 cm and base = 0.8 cm.

(The correct option is D).

The other two options are:

h = 2.75 cm / 1.76 cm = 1.5625 (option A)

h = 2 cm / 1.28 cm = 1.5625

All of these triangles have the same ratio between height and base.