Question

Question 9 - (3 marks available)

Tri


Use similar triangles to calculate the height, h cm, of triangle ABE.


10 cm


36 cm


20 cm

Answer 1

Image of the triangle is attached

Answer:

24 cm

Explanation:

If two triangles are similar, the corresponding sides must be in the same ratio.

From the diagram, the height of the triangle is 36cm.

But the height of triangle ABE = h,

To find the height of triangle BCD, let's subtract the height of triangle ABE from 36cm.

Therefore.

Height of BCD = 36 - h.

Since the triangles are similar and their corresponding sides have the same ratio, we have the expression:

`(b)/(h) = (b)/(h)`

Substituting figures, we have:

`(20)/(h) = (10)/(36-h)`

Cross multiplying, we have:

20(36-h) = 10 * h

720 - 20h = 10h

720 = 10h + 20h

720 = 30h

`h = (720)/(30)`

h = 24 cm

Therefore, the height of triangle ABE is 24cm