Question

The perimeter of a triangle is 24.8 yd. The longest side is twice the shortest side. The middle side is 2.4 yd longer than the shortest side. Write a mathematical equation and find the lengths of the sides.

a) Shortest side: 4.8 yd, Middle side: 7.2 yd, Longest side: 9.6 yd
b) Shortest side: 5.6 yd, Middle side: 8 yd, Longest side: 11.2 yd
c) Shortest side: 6.4 yd, Middle side: 9.6 yd, Longest side: 12.8 yd
d) Shortest side: 3.6 yd, Middle side: 6 yd, Longest side: 7.2 yd

Answer 1

The shortest side of the triangle is 5.6 yd, the middle side is 8 yd, and the longest side is 11.2 yd.

Step-by-step explanation:

Let's denote the shortest side of the triangle as 'x'. Based on the given information, the middle side would be 'x + 2.4' and the longest side would be '2x'. To find the lengths of the sides, we can set up an equation using the perimeter:

Perimeter = shortest side + middle side + longest side
24.8 = x + (x + 2.4) + 2x

Simplifying the equation:

24.8 = 4x + 2.4

Combining like terms:

24.8 - 2.4 = 4x

Dividing both sides by 4:

5.6 = x

So the shortest side is 5.6 yd, the middle side is 5.6 + 2.4 = 8 yd, and the longest side is 2 * 5.6 = 11.2 yd.