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:
[tex] \frac{b}{h} = \frac{b}{h} [/tex]
Substituting figures, we have:
[tex] \frac{20}{h} = \frac{10}{36-h} [/tex]
Cross multiplying, we have:
20(36-h) = 10 * h
720 - 20h = 10h
720 = 10h + 20h
720 = 30h
[tex]h = \frac{720}{30}[/tex]
h = 24 cm
Therefore, the height of triangle ABE is 24cm
