Question

The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side

Answer 1

Answer:

Shortest side=5, Largest side=13, Other side=12

Step-by-step explanation:

Let's define the shortest side of the triangle as x, since the other two sides are defined in terms of this one.

The longest side is 2 less than 3 times the shortest side, then it is 3 * x - 2.

The other side is 2 more than twice the shortest side, then it is 2 * x + 2.

By the problem directions, we know that the perimeter or sum of sides is 30.

x + 3x - 2 +  2*x + 2 = 30

Adding all the terms "with x" together and all terms "without x" together, we get...

6*x = 30

Solving for x (dividing both sides by 6), we get...

x = 30/6 = 5

Finally,

Shortest side: 5

Largest side: 3 * 5 - 2 = 13

Other side: 2 * 5 + 2 = 12

Answer 2

The length of each side of the triangle are 5 in, 12 in and 13 in respectively

Given:

Perimeter of the triangle = 30 in

let

shortest side = x

other side = 2x + 2

Longest side = 3x - 2

Perimeter of the triangle = shortest side + other side + Longest side

30 = x + (2x + 2) + (3x - 2)

30 = x + 2x + 2 + 3x - 2

30 = 6x

divide both sides by 6

x = 30 / 6

x = 5

Therefore,

shortest side = x

= 5 in

other side = 2x + 2

= 2(5) + 2

= 10 + 2

= 12 in

Longest side = 3x - 2

= 3(5) - 2

= 15 - 2

= 13 in

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