Question

I'll give brainliest for the first and correct answer! The perimeter of a triangle is 135. The sides have lengths a, b, and c. The ratio of a to b is 3:5 and the ratio of a to c is 6:11. Find the length of each side of the triangle.

Answer 1

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Answer:

  (a, b, c) = (30, 50, 55)

Step-by-step explanation:

If we rewrite the ratio of A to B so it has the same number of ratio units as in the ratio of A to C, we have ...

  A : B = 3 : 5 = 6 : 10

  A : C = 6 : 11

so ...

  A : B : C = 6 : 10 : 11

The total number of ratio units is 27. They stand for 135 real units, so each one stands for 135/27 = 5 real units.

Multiplying the last ratio statement by 5, we find the lengths of each of the sides.

  A : B : C = 6 : 10 : 11 = 30 : 50 : 55

The side lengths are (a, b, c) = (30, 50, 55).