Question

In trapezoid ABCD, AC is a diagonal and ∠ABC≅∠ACD. Find AC if the lengths of the bases BC and AD are 12m and 27m respectively.

Answer 1

Answer:

Length of diagonal is 18 m

Step-by-step explanation:

Given in trapezoid ABCD. AC is a diagonal and ∠ABC≅∠ACD. The lengths of the bases BC and AD are 12m and 27m. We have to find the length of AC.

Let the length of diagonal be x m

In ΔABC and ΔACD

∠ABC=∠ACD      (∵Given)

∠ACB=∠CAD      (∵Alternate angles)

By AA similarity theorem, ΔABC~ΔACD

∴ their corresponding sides are proportional

$\frac{x}{27}=\frac{12}{x}=\frac{AB}{CD}$

Comparing first two, we get

⇒ $\frac{x}{27}=\frac{12}{x}$

⇒ $x^2=27\times 12$

⇒ $x=\sqrt324=18$

hence, the length of diagonal is 18 m