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# (i) The sides of a triangle are in the ratio 7: 5: 3 and its perimeter is 30 cm. Find the lengths of sides. (ii) If the angles of a triangle are in the ratio 2: 3: 4, find the angles.

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This is an important ques from the Book ML Aggarwal class 10th,, chapter – 7, ratio and proportion.

In these both questions we have to. Distribute the total sum according to given fixed ratio.

In first question we have to distribute perimeter of triangle in the given ratio and in second ques we have to distribute total angle sum in given ratio

Question 16

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1. Solution:

(i) It is given that

Perimeter of triangle = 30 cm

Ratio among sides = 7: 5: 3

Here the sum of ratios = 7 + 5 + 3 = 15

We know that

Length of first side = 30 × 7/15 = 14 cm

Length of second side = 30 × 5/15 = 10 cm

Length of third side = 30 × 3/15 = 6 cm

Therefore, the sides are 14 cm, 10 cm and 6 cm.

(ii) We know that

Sum of all the angles of a triangle = 1800

Here the ratio among angles = 2: 3: 4

Sum of ratios = 2 + 3 + 4 = 9

So we get

First angle = 180 × 2/9 = 400

Second angle = 180 × 3/9 = 600

Third angle = 180 × 4/9 = 800

Hence, the angles are 400, 600 and 800.

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