Question

The lengths of the sides of quadrilateral EFGH are as follows: EF = 12 cm, FG = 6 cm, GH = 9 cm, and EH

Answer 1

The true statement about the side lengths of quadrilateral MNOP is (d) MP = OP = 11.25 cm because the scale factor for dilating quadrilateral EFGH is 1.25.

The side lengths of EFGH are given as:

$EF = 12\ cm$

$FG = 6\ cm$

$GH = 9\ cm$

$EH = 9\ cm$

Length NO is also given as:

$NO = 7.5\ cm$

Because both quadrilaterals are similar, then side NO corresponds to side FG.

The scale factor (k) from EFGH to MNOP is then calculated as:

$k = \frac{NO}{FG}$

$k = \frac{7.5}{6}$

$k = 1.25$

The side lengths of MNOP are then calculated using:

$MN = 12cm \times 1.25$

$MN = 15\ cm$

$OP = 9cm \times 1.25$

$O P = 11. 25 cm$

Also,

$MP = 11. 25 cm$

So, the true statement is (d)

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