Question

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

Answer 1

✬ Corresponding Side = 6 ✬

Step-by-step explanation:

Given:

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

To Find:

• What is the length of corresponding side of second triangle ?

Solution: If two triangle are similar then :- Ratio of corresponding sides of similar triangles is equal to the ratio of their perimeters.

Let first triangle be ∆ABC and second be ∆DEF.

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

Also,

• Side of first triangle i.e AB is 9 cm (given)
• AB will be. similar to DE i.e side of second triangle.

Ratio of sides will be

• AB/DE = BC/EF = AC/DF

Also these ratios will be equal to perimeter.

➨ AB/DE = BC/EF = AC/DF = 30/20

➨ 9/DE = 30/20

➨ 20 × 9 = 30 × DE

➨ 180 = 30 × DE

➨ 180/30 = DE

➨ 6 = DE

Hence, length of corresponding side of second triangle will be 6 cm.

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~ Note : Your question contains a mistake maybe you forgot to write perimeter of two similar triangle.

Answer 2

Answer :-

• 6cm

Given :-

• The perimeter of two similar triangles are 30cm and 20cm respectively and one side of the first triangle is 9cm long.

To Find :-

• The length corresponding side of the second triangle.

Solution :-

Let ∆ ABC and ∆ PQR are two similar triangles.

Now,

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

________________________________

• QR = 9
• BC = ?

In the similarity case,

→ Perimeter of ABC / Perimeter of PQR

= AB/PQ = BC/QR = AC/PR

[ ratio of their corresponding sides ]

According to question :-

→ 20/30 = BC/9

→ BC = 20/30 × 9

→ BC = 6cm

Hence, the length of the corresponding side of the second triangle is 6cm.