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
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.