Question

The perimeter of two similar triangles are 30 cm and 20 cm respectively if one side of the first triangle is 9 cm long find the length of the corresponding side of the second triangle.

Answer 1

Answer :

• Length of the corresponding side of the second triangle is 6cm

Given :

• Perimeter of two similar triangles are 30cm and 20cm respectively
• One side of the first triangle is 9cm

To find :

• The length of the corresponding side of the second triangle

Solution :

As we know that,

• If two triangles are similar then the ratio of corresponding sides of similar triangles is equal to the ratio of their perimeter (Theorem)

so,

• Let the first triangle be ∆ABC
• Second triangle be ∆DEF

Given that,

• Perimeter of ∆ABC = 30cm
• Perimeter of ∆DEF = 20cm

• One side of the first triangle is 9cm then ,
• AB will be similar to DE (side of second triangle)

Now Ratio of sides will be ,

• AB/DE = BC/EF = AC/DF

These ratios will be equal to Perimeter

Now,

⇢ AB/DE = BC/EF = AC/DF = 30/20

⇢ 9/DE = 30/20

⇢ 20 × 9 = 30 × DE

⇢ 180 = 30 × DE

⇢ 180/30 = DE

⇢ DE = 180/30

⇢ DE = 6

Hence , Length of the corresponding side of the second triangle is 6cm