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

Comparing first two, we get
⇒ 
⇒ 
⇒ 
hence, the length of diagonal is 18 m
Answer:
(x + 9)(x + 3)
Step-by-step explanation:
Factor 27 so that the factors, when combined, will equal 12:
x² + 12x + 27
x 9
x 3
(x + 9)(x + 3) is your answer.
Check: Use the FOIL method. Multiply the first two terms, the outside terms, the inside terms, and then the last two terms. Combine like terms:
(x + 9)(x + 3) = x² + 3x + 9x + 27 = x² + 12x + 27 (√)
~