how you do this:
The perimeter of an isosceles triangle is 36cm, and the area is 60cm. The length of the base is 3cm less than the length of a leg. Find the length of each side.
Let X = length of one of the legs.
Perimeter = 2X + (X - 3) = 36
3X = 39
X = 13
Check by inserting that value into the formula for the area.
I hope this helps. Thanks for asking.
x= 13
To solve this problem, we can use the properties of an isosceles triangle and the formulas for its perimeter and area.
Let's assume that the length of each leg of the triangle is "x" cm. According to the given information, the length of the base is 3 cm less than the length of each leg, so the length of the base is (x - 3) cm.
The perimeter of a triangle is the sum of the lengths of all three sides. For an isosceles triangle, since two sides are of equal length (legs), we can calculate the perimeter as: 2 * leg length + base length.
In this case, the perimeter is given as 36 cm, so we can write the equation as:
2x + (x - 3) = 36
Next, we can solve this equation to find the value of "x" (the length of each leg).
2x + x - 3 = 36
3x - 3 = 36
3x = 36 + 3
3x = 39
x = 39 / 3
x = 13
So, the length of each leg is 13 cm.
Now, we can calculate the length of the base:
x - 3 = 13 - 3 = 10
Hence, the length of each side of the triangle is 13 cm for the legs and 10 cm for the base.