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Two triangles are shown. The first triangle has sides x, 6 cm, and 12 cm, and the second triangle has corresponding sides 20 cm, 8 cm, and 16 cm. The two triangles above are similar. Find x using the ratio of the sides 12 cm and 16 cm: x 20 = 12 16 . Show your work. Find x using the ratio of the sides 6 cm and 8 cm. Show your work. Explain why the answers to (a) and (b) should be the same.

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Answer:

Given the two triangles are shown:

First triangle has sides x cm , 6 cm and 12 cm.

and

Second  triangle has sides 20 cm , 8 cm and 16 cm.

Since, the given two triangles are Similar.

⇒there corresponding sides are in proportion.

i,e

[tex]\frac{x}{20}=\frac{6}{8}=\frac{12}{16}[/tex]

(a)

[tex]\frac{x}{20}=\frac{12}{16}[/tex]

Solve for x;

By cross multiply we have;

[tex]16x = 240[/tex]

Divide both sides by 16 we get;

[tex]x = 15[/tex] cm

(b)

Find x using the ratio sides:

[tex]\frac{6}{8} = \frac{x}{20}[/tex]

By cross multiply we have;

[tex]120 = 8x[/tex]

Divide both sides by 8 we get;

[tex]15 = x[/tex]

or

[tex]x = 15[/tex] cm

The value of x =15 cm in both a and b is same because the given two triangles are similar,

by definition of similarity, the given triangles have their corresponding sides are in proportion.

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