**Chapter 1 Similarity Set 1.4**

## Chapter 1 Similarity Set 1.4

**Question 1.The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas.Solution:**

Let the corresponding sides of similar triangles be S

_{1}and S

_{2}.

Let A

_{1}and A

_{2}be their corresponding areas.

∴ Ratio of areas of similar triangles = 9 : 25

**Question 2.If ∆ABC ~ ∆PQR and AB : PQ = 2:3, then fill in the blanks.Solution:**

**Question 3.If ∆ABC ~ ∆PQR, A(∆ABC) = 80, A(∆PQR) = 125, then fill in the blanks.Solution:**

**Question 4.∆LMN ~ ∆PQR, 9 × A(∆PQR) = 16 × A(∆LMN). If QR = 20, then find MN.Solution:**

**Question 5.Areas of two similar triangles are 225 sq. cm. and 81 sq. cm. If a side of the smaller triangle is 12 cm, then find corresponding side of the bigger triangle.Solution:**

Let the areas of two similar triangles be A

_{1}and A

_{2}.

A

_{1}= 225 sq. cm. A

_{2}= 81 sq. cm.

Let the corresponding sides of triangles be S

_{1}and S

_{2}respectively.

S

_{1}= 12 cm

∴ The length of the corresponding side of the bigger triangle is 20 cm.

**Question 6.∆ABC and ∆DEF are equilateral triangles. If A(∆ABC): A(∆DEF) = 1:2 and AB = 4, find DE.Solution:**

In ∆ABC and ∆DEF,

**Question 7.In the adjoining figure, seg PQ || seg DE, A(∆PQF) = 20 sq. units, PF = 2 DP, then find A (꠸ DPQE) by completing the following activity.Solution:**

A(∆PQF) = 20 sq.units, PF = 2 DP, [Given]

Let us assume DP = x.

∴ PF = 2x