Quadrilateral ABCD is similar to quadrilateral EFGH the length of the three longest side in quadrilateral ABCD are 24 feet 16 feet and 12 feet long if the two shortest sides of quadrilateral EFGH feet long and 18 feet long how long is the fourth side on quadrilateral ABCD ?

check the picture below

solve for "x"

since we know the two smallest sides for EFGH are 9 and 18, 9 is the smallest of all, and 18 is the next small

thus, for the the quadrilateral ABCD, the smallest is "x" and the next small is given, is 12, since that's smaller than 16 or 24

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MrRoyal MrRoyal · Answer 2 · 2021-08-10T14:05:36+02:00

When all sides of a quadrilateral are transformed, the resulting quadrilateral will be similar to the transformed quadrilateral. The fourth side of ABCD is 6 feet

We have the lengths of ABCD in descending order to be:

[tex]Side\ 1 = 24[/tex]

[tex]Side\ 2 = 16[/tex]

[tex]Side\ 3 = 12[/tex]

We have the lengths of EFGH in ascending order to be:

[tex]Side\ 4 = 9[/tex]

[tex]Side\ 3 = 18[/tex]

The missing side of ABCD is the fourth side, and it can be solved using the following equivalent ratios:

Side 4 : Side 3 of ABCD = Side 4: Side 3 of EFGH

Substitute the values of the known sides

[tex]Side\ 4 : 12 = 9 : 18[/tex]

Express as fraction

[tex]\frac{Side\ 4 }{ 12} = \frac{9}{ 18}[/tex]

Multiply both sides by 12

[tex]Side\ 4 = \frac{9}{ 18} \times 12[/tex]

[tex]Side\ 4 = \frac{1}{2} \times 12[/tex]

[tex]Side\ 4 = 6[/tex]

Hence, the fourth side of ABCD is 6 feet

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