how long are the congruent legs of isosceles triangle if its base and altitude to the base are 12cm and 8 cm respectively?
miss sue can u pls help me?
To find the lengths of the congruent legs of an isosceles triangle, we need to apply the Pythagorean Theorem.
In an isosceles triangle, the base divides the triangle into two congruent right triangles, each with a leg equal to half the length of the base and the altitude as the other leg.
Given that the base of the triangle is 12 cm and the altitude to the base is 8 cm, we can use the Pythagorean theorem to find the length of the congruent legs:
Let's call the length of the congruent legs 'x'.
Using the Pythagorean theorem:
x^2 = (1/2 * 12)^2 + 8^2
x^2 = 6^2 + 64
x^2 = 36 + 64
x^2 = 100
Taking the square root of both sides:
x = 10
Therefore, the lengths of the congruent legs of the isosceles triangle are both 10 cm.