Question

the perimeter of a triangle is 75 units. the sides have lengths a, b, c. the ratio of b to a is 4:5,and the ratio of c to a is 7:5. find the lengths of each side.

Answer 1

a = 23.5, b = 18.8 and c = 32.9

Step-by-step explanation:

The sides of the triangle are a, b and c

Hence a + b + c = 75 ...1

If the ratio of b to a is 4:5, then;

b/a = 4/5

4a = 5b

b = 4a/5 ...2

Also

Ratio of c to a is 7:5, then;

c/a = 7/5

7a = 5c

c = 7a/5 .... 3

Substitute 2 and 3 into 1:

From 1: a + b + c = 75

a + 4a/5 + 7a/5 = 75

Multiply through by 5

5a + 4a + 7a = 375

16a = 375

a = 375/16

a = 23.5

Get b;

b = 4a/5

b = 4(23.5)/5

b = 18.8

Get c:

c = 7a/5

c = 7(23.5)/5

c = 32.9

Hence a = 23.5, b = 18.8 and c = 32.9