If perimeter of an isoceles triangle is 37 inches, and the lengths of both sides are 6 inches less than 3 times the length of the base, what is the length of all three sides?

You need to translate the information they give you to algebraic equations. Remember, an isosceles triangle has 2 sides equal to eachother and one not. So, if you call x the length of the sides that are equal, and y the length of the base, then you can make the first equation: 2x + y = 37.

CAn you figure out what the second equation is??

To find the lengths of all three sides of the isosceles triangle, we can use the given information that the perimeter is 37 inches and that both sides are 6 inches less than 3 times the length of the base.

Let's assume the length of the base of the triangle is x inches.

According to the given information, the lengths of both sides are 6 inches less than 3 times the length of the base, so each side has a length of (3x - 6) inches.

The perimeter of a triangle is the sum of the lengths of all three sides. Therefore, we can write the equation:

Perimeter = Base + Side1 + Side2

Using the values we have, we can substitute them into the equation:

37 = x + (3x - 6) + (3x - 6)

Now, we can simplify the equation and solve for x:

37 = x + 3x - 6 + 3x - 6
37 = 7x - 12

Next, we isolate the variable by adding 12 to both sides of the equation:

37 + 12 = 7x - 12 + 12
49 = 7x

To find the value of x, we divide both sides of the equation by 7:

49 / 7 = 7x / 7
7 = x

Now that we have the value of x, which is 7, we can substitute it into the expression for the length of the sides:

Side1 = (3x - 6) = (3 * 7 - 6) = 15 inches
Side2 = (3x - 6) = (3 * 7 - 6) = 15 inches

So, the length of all three sides of the isosceles triangle is:

Base = x = 7 inches
Side1 = 15 inches
Side2 = 15 inches