Question

The area of the triangle shown is represented by A=s(s−21)(s−17)(s−10)−−−−−−−−−−−−−−−−−−−−√, where s is equal to half the perimeter. What is the height h of the triangle?

Answer 1

Answer:

9.88 units

Step-by-step explanation:

We are given that area of triangle  is given by

$A=\sqrt{s(s-21)(s-17)(s-10)}$

s=Half perimeter

By comparing with

$A=\sqrt{s(s-a)(s-b)(s-c)}$

We get

a=21

b=17

c=10

$s=\frac{a+b+c}{2}=\frac{21+17+10}{2}=24$

Now, the area

$A=\sqrt{24(24-21)(24-17)(24-10)}$

A=84

Area of triangle, $A=\frac{1}{2}\times bh$

b=17

$84=\frac{1}{2}(17)(h)$

$h=\frac{84\times 2}{17}$

$h=9.88 units$

Hence, the height of the triangle=9.88 units