the perimeter of a triangle is 79.75 inches. the second side of the triangle is half as big as the first side. the third side is 7.25 in greater than the first side
what is the length of the longest side of the triangle?
Let x = first side, then x/2= second and x+7.25 = third.
x + x/2 + x+7.25 = 79.75
Solve for x, then x+7.25.
To find the length of the longest side of the triangle, we can use the information given about the relationship between the sides. Let's go step by step:
Let's assume the length of the first side is x inches.
According to the given information, the second side is half as big as the first side, so its length is x/2 inches.
The third side is 7.25 inches greater than the first side, so its length is x + 7.25 inches.
The perimeter of a triangle is the sum of the lengths of all three sides. So we can write the equation:
Perimeter = first side + second side + third side
Substituting the given values, we have:
79.75 inches = x + x/2 + x + 7.25
To solve this equation, we need to combine like terms:
79.75 inches = 2.5x + 7.25
Next, let's isolate x by subtracting 7.25 from both sides:
72.5 inches = 2.5x
Now, divide both sides by 2.5 to solve for x:
x = 72.5 inches / 2.5
x = 29 inches
So, the length of the first side is 29 inches.
Now, we can find the length of the longest side (third side) by substituting the value of x into the equation:
Longest side = x + 7.25
Longest side = 29 inches + 7.25 inches
Longest side = 36.25 inches
Therefore, the length of the longest side of the triangle is 36.25 inches.