Question

The perimeter of a triangle is 40 inches. Twice the length of the longest side minus the length of the shorted side in 30 inches. The sum of the length of the longest side and twice the sun of both the other side lengths is 61 inches. Find the side lengths

Answer 1

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Answer:

8 inches, 13 inches, 19 inches

Explanation:

Let's identify the side lengths (shortest to longest) as a, b, c. Then we have ...

a + b + c = 40 . . . . . . perimeter

2c -a = 30

2a +2b +c = 61

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Subtracting the third equation from twice the first gives ...

2(a +b +c) -(2a +2b +c) = 2(40) -(61)

c = 19 . . . . . simplify

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

2(19) -a = 30

38 -30 = a = 8 . . . . add a-30

Then the first equation reveals b:

8 + b + 19 = 40

b = 40 -27 = 13

The side lengths are 8 in, 13 in, and 19 in.