Question

Given ΔADC and ΔAEB, What is AE?

Answer 1

Answer:

AE = 43.2 units

Step-by-step 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:

$\dfrac{AB}{AC} = \dfrac{AE}{AD}\\\Rightarrow \dfrac{33}{55} = \dfrac{x}{x+72}\\\Rightarrow 55x = 33 \times 72\\\Rightarrow x = \dfrac{3\times 72}{5}\\\Rightarrow x = 43.2\ units$

So, AE = 43.2 units