Question

Quadrilateral ABCD is similar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 24 feet, 16 feet, 12 feet long. If the

two shortest sides of quadrilateral EFGH are 9 feet long and 18 feet long, how long is the 4th side quadrilateral ABCD ?
A. 16 feet
B. 20 feet
C. 24
D. 36

Answer 1

The length of the fourth side of quadrilateral ABCD is 24 feet.

Step-by-step explanation:

Since quadrilateral ABCD is similar to quadrilateral EFGH, the corresponding sides of the two quadrilaterals are in the same ratio. Let's find the ratio between the lengths of sides ABC and EFG:

ABC: EFG = 24: 9 = 8: 3

Now we can find the length of the fourth side of quadrilateral ABCD. Since the length of side EFG is 9 feet, the length of the corresponding side ABC is:

9 x (8/3) = 24 feet

Therefore, the length of the fourth side of quadrilateral ABCD is 24 feet.

Answer 2

Step-by-step explanation:

Given that quadrilateral ABCD is similar to quadrilateral EFGH.

Hence we have lengths are proportional

ABCD has sides if arranged from larger to smaller the third one is 12 feet.

Similarly if EFGH are arranged from small to large the second one is 18 feet.

Thus we have the sides 12 and 18 would be corresponding sides.

Proportionality = 12;18 = 2:3

Now left over is the smallest side of ABCD.

if x is the smallest side

then x: 9 = 2:3

Solving we have

x =6 feet

THus answer is 6 feet

The answers given are wrong as the smallest side cannot exceed other side lengths.