Question

The perimeter of two similar triangles are 30 cm and 20 cm respectively .If one side of the first triangle is 12 cm , determine the corresponding side of the second triangle .
need a correct explanation

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Answer 1

Answer:

Step-by-step explanation:

Let the required side be 'x'

Following this theorem, just plug the values

30/20 = 12/x

3/2 = 12/x

x = 24/3

x = 8

Answer 2

Given:-

• Perimeter of two similar triangles are 30 cm and 20 cm.
• One side of first triangle is 12 cm.

Find:-

Corresponding side of the second triangle.

Solution:-

Given that two triangles are similar means, ratio of the perimeters of the triangle is equal to ratio of their corresponding sides.

Let the -

• corresponding side of second triangle be "x"

So,

$\sf{\frac{Perimeter \:of\:first\:triangle}{Perimeter \:of\:second\:triangle} \:=\:\frac{Length \:of\:corresponding \:side\:of\:first \:triangle}{Length \:of\:corresponding \:side\:of\:second \:triangle}}$

Substitute the known values in above formula

⇒ $\sf{\dfrac{30}{20}\:=\:\dfrac{12}{x}}$

⇒ $\sf{\dfrac{3}{2}\:=\:\dfrac{12}{x}}$

Cross-multiply them

⇒ $\sf{3x\:=\:12\:\times\:2}$

⇒ $\sf{3x\:=\:24}$

⇒ $\sf{x\:=\:8}$

•°• Corresponding side of second triangle is 8 cm.