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.

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

Comparing first two, we get

⇒

⇒

⇒

hence, the length of diagonal is 18 m

5/20 so 25%

step-by-step explanation: