The perimeter of an isosceles triangle is 37 in. The lengths of the two
equal legs are 6 in. less than 3 times the length of the base. Find the lengths of the three sides.
37=2L+2W
W=3W-6
do i have this equation wrote right
when i try to solve it
the answers i get is
w=3
l=15.5
I feel like i maybe missing some thing here can anyone help me
Your equation 37=2L+2W would be used for a rectangle, not a triangle.
let the base be x in
then the other sides are 3x-6 each
now add them up
3x-6 + 3x-6 + x = 37
..
..
x=7
so the base is 7, the other sides are 15 each.
everything checks out!
To solve this problem, you need to correctly set up the equations and solve for the unknowns. Here's the correct approach:
Let's assume the base of the triangle is represented by "x" inches. According to the problem, the two equal legs are 6 inches less than 3 times the length of the base. Therefore, the length of each equal leg is (3x - 6) inches.
The perimeter of an isosceles triangle is calculated by adding up the lengths of all three sides. So, we can set up the equation:
x + (3x - 6) + (3x - 6) = 37
Now, let's solve this equation:
Combine like terms:
x + 3x + 3x - 6 - 6 = 37
7x - 12 = 37
Add 12 to both sides to isolate the variable:
7x - 12 + 12 = 37 + 12
7x = 49
Divide both sides by 7 to solve for x:
7x / 7 = 49 / 7
x = 7
Therefore, the base of the triangle is 7 inches.
Substitute the value of x into the expressions for the equal legs:
Legs = 3x - 6
Legs = 3(7) - 6
Legs = 15
So, each equal leg of the triangle is 15 inches.
In summary, the lengths of the three sides of the isosceles triangle are:
Base = 7 inches
Equal legs = 15 inches