Mathematics: 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.

Two triangles are shown. the first triangle has

sweetmochi13

09.03.2022

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

$\frac{x}{20}=\frac{6}{8}=\frac{12}{16}$

(a)

$\frac{x}{20}=\frac{12}{16}$

Solve for x;

By cross multiply we have;

16x = 240

Divide both sides by 16 we get;

x = 15 cm

(b)

Find x using the ratio sides:

$\frac{6}{8} = \frac{x}{20}$

By cross multiply we have;

120 = 8x

Divide both sides by 8 we get;

15 = x

x = 15 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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