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:
[tex]EF = 12\ cm[/tex]
[tex]FG = 6\ cm[/tex]
[tex]GH = 9\ cm[/tex]
[tex]EH = 9\ cm[/tex]
Length NO is also given as:
[tex]NO = 7.5\ cm[/tex]
Because both quadrilaterals are similar, then side NO corresponds to side FG.
The scale factor (k) from EFGH to MNOP is then calculated as:
[tex]k = \frac{NO}{FG}[/tex]
[tex]k = \frac{7.5}{6}[/tex]
[tex]k = 1.25[/tex]
The side lengths of MNOP are then calculated using:
[tex]MN = 12cm \times 1.25[/tex]
[tex]MN = 15\ cm[/tex]
[tex]OP = 9cm \times 1.25[/tex]
[tex]O P = 11. 25 cm[/tex]
Also,
[tex]MP = 11. 25 cm[/tex]
So, the true statement is (d)
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