Question

The sides of a triangle have lengths x + 3, 4(x - 13), and 3 over 4 x. The perimeter of the triangle is 3x +6. What is the length of the shortest side of the triangle?

Numbers to represent the answer:
1, 2, 3, 4, 5, 6, 7, 8, 9, 0

Answer 1

shortest side = 15

Explanation:

The question is a bit ambiguous. Do you mean (3/4) x or do you mean 3/(4x)?

I'll take it to be the first one.

(x + 3) + 4(x - 13) + (3/4)x = 3x + 6 Remove the brackets on the left

x + 3 + 4x - 52 + 0.75 x = 3x + 6 Combine

5.75x - 49 = 3x + 6 Subtract 3x from both sides.

2.75x - 49 = 6 Add 49 to both sides

2.75x = 55 Divide by 2.75

x = 55/ 2.75

x = 20

Now for the shortest side

x + 3 = 23

4(x - 13) = 4(20 - 13) = 4*7 = 28

(3/4)*20 = 15

The shortest side = 15