Question

use the geometric mean (leg) theorem. what is the value of a?

Answer 1

$\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}$

Actually Welcome to the concept of Geometric Mean (leg) theorem.

So according to the rule, we know that, here altitude = h and left side is 6 and right side is 14 , so we get as,

==> altitude/left = right/altitude

==> h/6 = 14/h

==> h^2 = 14*6

==> h^2 = 84

2.) so now we apply the Pythagoras theorem in triangle ∆DCB

so we get as,

==> (14)^2 + h^2 = a^2

==> 196 + 84 = a^2

==> 280 = a^2

==> a = √280

==> after simplified => a = √70*4

==> a = 2√70 units

hence the correct answer is a => 2√70 units.