Answer:
The length of the side measuring (5x) in. is 35 inches
The length of the side measuring (7x + 1) in. is 50 inches
The length of the side measuring (7x + 8) in. is 57 inches
Explanation:
To find the perimeter of a triangle, we sum all three sides of the triangle.
In this case, we already know the perimeter, so we can set up a linear equation where we add each side and equal it to 142:
(5x) + (7x + 1) + (7x + 8) = 142
Combine like terms.
(5x + 7x +7x) + (1 + 8) = 142
19x + 9 = 142
Simplify by subtracting each side by 9.
19x = 13
Simplify further by dividing each side by 19.
x = 7
Now that we know the value of x = 7, we can go back and plug the value into the expression for each side to find its length
5(7) = 35
7(7) + 1 = 50
7(7) + 8 = 57
To check our work, we can add all three sides to ensure they equal 142.
35 + 50 + 57 = 142