Question

The lengths of the sides of a triangle are x+5, 2x+7, and 4x+1. The perimeter of the triangle is 41 cm. What are the lengths of each side?

A. x+5 = 9 cm, 2x+7 = 11 cm, 4x+1 = 21 cm
B. x+5 = 11 cm, 2x+7 = 21 cm, 4x+1 = 9 cm
C. x+5 = 21 cm, 2x+7 = 11 cm, 4x+1 = 9 cm
D. x+5 = 9 cm, 2x+7 = 21 cm, 4x+1 = 11 cm

Answer 1

To find the lengths of the sides of the triangle, we need to set up an equation using the given information. The perimeter of a triangle is the sum of the lengths of its sides, so we have the equation (x+5) + (2x+7) + (4x+1) = 41. Solving for x, we find x = 4. Substituting x = 4 back into the lengths of the sides, we get x+5 = 9 cm, 2x+7 = 15 cm, and 4x+1 = 17 cm.

Step-by-step explanation:

To find the lengths of the sides of the triangle, we need to set up an equation using the given information. The perimeter of a triangle is the sum of the lengths of its sides, so we have the equation (x+5) + (2x+7) + (4x+1) = 41. Simplifying this equation, we get 7x + 13 = 41. Solving for x, we find x = 4.

Substituting x = 4 back into the lengths of the sides, we get:

x+5 = 4+5 = 9 cm

2x+7 = 2(4)+7 = 15 cm

4x+1 = 4(4)+1 = 17 cm

Therefore, the lengths of the sides of the triangle are x+5 = 9 cm, 2x+7 = 15 cm, and 4x+1 = 17 cm. So, the correct answer is option A.