Question

Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 20 feet, 18 feet, and 14 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 5 feet long, how long is the 2nd longest side on quadrilateral EFGH?

Answer 1

First, let's list the lengths of the sides in descending order.

Lengths of sides of quadrilateral ABCD: 20, 18, 14, a

Lengths of sides of quadrilateral EFGH: b, c, 6, 5

From the listings above, we see that he sides measuring 14 and 6 are corresponding.

We are looking for c which corresponds to 18.

14 is to 6 is as 18 is to c

14/6 = 18/c

7/3 = 18/c

7c = 3 * 18

7c = 54

c = 54/7 = 7 5/7

Answer: 7 5/7 feet

Answer 2

Answer:  The length of the second longest side of quadrilateral EFGHJ is 7.71 feet.

Step-by-step explanation:  Given that the quadrilateral ABCD is similar to quadrilateral EFGH.

The lengths of the three longest sides in quadrilateral ABCD are 20 feet, 18 feet, and 14 feet long and the two shortest sides of quadrilateral EFGH are 6 feet long and 5 feet long.

We are to find the length of the second longest side of quadrilateral EFGH.

Let x, y, z, w and x', y', z', w' represents the respective lengths of the quadrilaterals ABCD and EFGH is descending order.

Then, we have

x = 20 feet, y = 18 feet, z = 14 feet, z'=6 feet   and   w' = 5 feet.

We know that

the corresponding sides of two similar figures are proportional. so, for the given quadrilaterals, we have

$\dfrac{x}{x'}=\dfrac{y}{y'}=\dfrac{z}{z'}=\dfrac{w}{w'}\\\\\\\Rightarrow \dfrac{20}{x'}=\dfrac{18}{y'}=\dfrac{14}{6}=\dfrac{w}{5}\\\\\\\Rightarrow 14y'=18\times6\\\\\Rightarrow y'=\dfrac{108}{14}\\\\\Rightarrow y'=7.71.$

Thus, the length of the second longest side of quadrilateral EFGHJ is 7.71 feet.