Question

Quadrilateral ABCD is similar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 4th side on quadrilateral ABCD?

Answer 1

check the picture below.

solve for "x".

Answer 2

Answer: 15 feet

Step-by-step explanation:

Given: Quadrilateral ABCD is similar to quadrilateral EFGH.

If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long.

Let x be the shortest side of quadrilateral ABCD .

The measurement of sides of  quadrilateral ABCD arranged in order :-

60 feet , 40 feet, 30 feet and x feet.

We know that the corresponding sides of two similar polygons are proportional.

⇒ The two shortest sides of quadrilateral ABCD is proportional to the two proportional sides of quadrilateral EFGH.

⇒$\dfrac{6}{12}=\dfrac{x}{30}\\\\\Rightarrow\ x=\dfrac{30\times6}{12}=15$

Hence, the length of the 4th sides of quadrilateral ABCD = 15 feet.