Question

An isosceles triangle with legs of 9 cm and a base of 10 cm in length has a median drawn from its vertex angle to its base. What is the length of this segment?

Answer 1

Answer: $7.48\ cm$

Step-by-step explanation:

Given

The equal side of two isosceles triangle are $9\ cm$ long

Base of the triangle is $10\ cm$ long

Median divides the base into two equal halves

from the figure, it can be written

$\Rightarrow 9^2=5^2+h^2\\\Rightarrow h^2=9^2-5^2\\\Rightarrow h=\sqrt{81-25}\\\Rightarrow h=\sqrt{56}\\\Rightarrow h=7.48\ cm$

The length of the segment is $7.48\ cm$