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
It seems like you have made a small error in your equations. Let me explain step by step how to solve this problem correctly.
First, let's define the variables:
Let W be the length of the base of the isosceles triangle.
Let L be the length of the two equal legs of the triangle.
Based on the given information, we can write two equations:
1) Perimeter equation: The perimeter of the triangle is 37 inches, so the sum of all three sides is 37. In an isosceles triangle, the two equal sides have the length L, and the base has the length W. Therefore, we can write the perimeter equation as:
37 = 2L + W + W
2) Length equation: The lengths of the two equal legs are 6 inches less than 3 times the length of the base. In other words, L = 3W - 6.
Now, let's solve these equations to find the lengths of the sides:
From the length equation, we can express L in terms of W:
L = 3W - 6
Substituting this expression for L into the perimeter equation, we have:
37 = 2(3W - 6) + W + W
Simplifying the equation:
37 = 6W - 12 + 2W
37 = 8W - 12
Bringing the constant term to the other side of the equation:
8W = 37 + 12
8W = 49
Dividing both sides of the equation by 8:
W = 49/8 = 6.125
Now that we have the value of W, we can substitute it back into the length equation to find L:
L = 3(6.125) - 6 = 18.375 - 6 = 12.375
Therefore, the lengths of the three sides of the isosceles triangle are:
Base (W) = 6.125 inches
Equal legs (L) = 12.375 inches
So your calculation is incorrect. The correct lengths are W = 6.125 inches and L = 12.375 inches.