Answer:
x = 3*sqrt(15) = 11.61895
Step-by-step explanation:
Properties of the Triangle.
The triangle is isosceles It has 2 equal sides (24)
x meets the base at a right angle Given
An altitude also is a median Property of Isosceles triangle
A median divides a base into 2 equal segments Isoceles triangle
42 /2 = 21 Above Property
Find x
Formula
a^2 + b^2 = c^2
Givens
a = x
b = 21
c = 24
Solution
a^2 + b^2 = c^2 Substitute for a,b and c
x^2 + 21^2 = 24^2
x^2 + 441 = 576 Subtract 441 from both sides.
x^2 = 576 - 441
x^2 = 135
135: 3*3*3*5
Take the square root of both sides
x = sqrt(135)
sqrt(135) = sqrt(3 * 3 * 3 * 5). For every pair of primes, you can take out 1 prime and throw the other one away. You are left with something under the root sign.
x = 3 * sqrt(15) Answer
