The first side of a triangle is 7 cm shorter than twice the second side. The third side is 4 cm longer than the second side. The perimeter is 77 cm. Which equation represents how to find each side?
a) 4x + 3 = 77
b) 3x - 11 = 77
c) 3x - 3 = 77
d) 4x - 3 = 77
add up the sides to get the perimeter:
x-7 + x + x+4 = 77
now simplify
To find the equation that represents how to find each side of the triangle, we need to analyze the given information.
Let's assume that the second side of the triangle is represented by the variable x.
According to the problem, the first side of the triangle is 7 cm shorter than twice the second side. So, the first side is equal to (2x - 7) cm.
The third side of the triangle is 4 cm longer than the second side. Therefore, the third side is equal to (x + 4) cm.
The perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 77 cm. Thus, we can set up the following equation:
(2x - 7) + x + (x + 4) = 77
Simplifying this equation:
2x - 7 + x + x + 4 = 77
4x - 3 = 77
Therefore, the equation that represents how to find each side of the triangle is d) 4x - 3 = 77.