ABC  DEF. Find the length of median CP. please help me out!

The measured sides are 24 and 32 units long. It means that the larger triangle is [tex]\frac{32}{24} =\frac 43[/tex] times bigger than the smaller one. In particular, all linear measures are scaled of the same ratio: for medians we can write

[tex]FQ= \frac 43 CP \rightarrow 3FQ=4CP[/tex]

At this point we replace both segments with their lengths and solve for x. Once we find x, we can determine the length of CP.

[tex]3(2x+8)=4(3x-12)\\6x+24=12x-48 \rightarrow 6x=72 \rightarrow x=13\\CP = 3(13)-12 =36-12=24[/tex]

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-05-31T10:53:37+02:00

The length of the median CP is 24 units if the triangle ABC and triangle DEF are similar, option (C) is correct.

What is the similarity law for triangles?

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

The ratio of the sides:

DE/AB = 32/24 = 4/3

Similarly, the ratio of the sides:

QF/CP = 4/3

3QF = 4CP

3(2x + 8) = 4(3x - 12)

6x + 24 = 12x - 48

6x = 72

x = 12

CP = 3(12)—12 = 24 units

Thus, the length of the median CP is 24 units if the triangle ABC and triangle DEF are similar, option (C) is correct.

Learn more about the similarity of triangles here:

brainly.com/question/8045819

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