Question

An altitude is drawn from the vertex of an isosceles triangle, forming a right angle

and two congruent triangles. As a result, the altitude cuts the base into two equal
segments. The length of the altitude is 11 inches, and the length of the base is 6
inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.

Answer 1

Since the altitude cuts the base into two equal segments, each segment has a length of 6/2 = 3 inches.

Since the triangle is isosceles, the length of each of the two equal sides can be found using the Pythagorean theorem:

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse (in this case, the length of the equal side).

We can substitute the known values:

a = 3 (half the length of the base)
b = 11 (the length of the altitude)

So:

3^2 + 11^2 = c^2
9 + 121 = c^2
130 = c^2
c = sqrt(130) = 11.4

Finally, we can find the perimeter of the triangle:

P = c + c + 6
P = 11.4 + 11.4 + 6
P = 29.8

Rounding to the nearest tenth of an inch, the perimeter of the triangle is 29.8 inches.