Question

Given ΔADC and ΔAEB, What is AE?

Answer 1

AE = 43.2 units

Explanation:

As per the given question image, it can be seen that in the
`\triangle ADC \text { and }\triangle AEB :`

1.
`\angle B = \angle C = 90^\circ`

2.
`\angle A` is common to both the triangles.

3. Two angles are common, so the third angle
`\angle E` is also equal to
`\angle D`.

All the three angles in the
`\triangle ADC \text { and }\triangle AEB` are equal to each other, hence the triangles are similar.

As per the property of similar triangles, the ratio of their sides will be equal.

AB : AC = AE : AD

AC = 88 units

BC = 55 units

AB = AC - AB = 33 units

Let side AE =
`x` units

Side AD = AE + ED

So, AD =
`x + 72`

Using the ratio:

`(AB)/(AC) = (AE)/(AD)\\\Rightarrow (33)/(55) = (x)/(x+72)\\\Rightarrow 55x = 33 * 72\\\Rightarrow x = (3* 72)/(5)\\\Rightarrow x = 43.2\ units`

So, AE = 43.2 units