Question

Question 9 - (3 marks available)

Answer 1

Image of the triangle is attached

Answer:

24 cm

Step-by-step 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:

$\frac{b}{h} = \frac{b}{h}$

Substituting figures, we have:

$\frac{20}{h} = \frac{10}{36-h}$

Cross multiplying, we have:

20(36-h) = 10 * h

720 - 20h = 10h

720 = 10h + 20h

720 = 30h

$h = \frac{720}{30}$

h = 24 cm

Therefore, the height of triangle ABE is 24cm