The lengths of the sides of a triangle are in the ratio 3 : 7 : 5. The perimeter of the triangle is 90 inches. What is the length of the largest side
let the sides be 3x, 7x, and 5x. Then
3x+7x+5x = 90
solve for x, sub into my definitions for the longest side.
2(3x+7x+5x) = 90
oops. my bad. I was thinking of a rectangle and hit submit before I saw that there were three sides!
To find the length of the largest side of the triangle, we can first assign variables to the ratios given. Let's call the lengths of the sides 3x, 7x, and 5x.
We are also given that the perimeter of the triangle is 90 inches. The perimeter of a triangle is the sum of the lengths of its sides. So we can set up the equation:
3x + 7x + 5x = 90
Combining like terms, we have:
15x = 90
Dividing both sides of the equation by 15, we find:
x = 6
Now we can substitute the value of x back into the equation to find the lengths of the sides:
3x = 3 * 6 = 18 inches
7x = 7 * 6 = 42 inches
5x = 5 * 6 = 30 inches
The lengths of the sides of the triangle are 18 inches, 42 inches, and 30 inches. Therefore, the length of the largest side is 42 inches.