Question

A little help on this math problem?

Answer 1

If you know Heron's formula, this is easy.

$\text{area}=\sqrt{s(s-6)(s-10)(s-14)}=15\sqrt3$

where $s=\dfrac{6+10+14}2=15$ is the semiperimeter of the triangle.

The area is also equal to half the product of the base and height of the triangle, which happen to be

$15\sqrt3=\dfrac{14x}2\implies x=\dfrac{15\sqrt3}7\approx3.711$

so the answer is B.