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The perimeter of a triangle is 74 cm. The longest side is 8 cm less than the sum of the other two sides. Twice the shortest side is 5 cm less than the longest side. Find the length of each side of the triangle.

Sagot :

sqdancefan

Answer:

  14 cm, 27 cm, 33 cm

Step-by-step explanation:

You want the three sides of a triangle such that their sum is 74 cm, the longest is 8 cm less than the sum of the other two, and twice the shortest is 5 cm less than the longest.

Setup

Let a, b, c represent the lengths of the sides in order from shortest to longest. The given relations are ...

  a + b + c = 74

  c = a + b -8

  2a = c - 5

Solution

Adding 8 to the second equation and using that to substitute for (a+b) in the first, we have ...

  c +8 = a +b
  (c +8) +c = 74
  2c = 66 . . . . . . . . . subtract 8
  c = 33 . . . . . . . . . . divide by 2

Using this in the third equation, we have ...

  2a = 33 -5
  a = 28/2 = 14 . . . . . . divide by 2

Either of the first two equations can be used to find b.

  14 +b +33 = 74
  b = 74 -47 = 27

The lengths of the sides of the triangle are 14 cm, 27 cm, and 33 cm.

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