# Triangle question- 5th Jan'16

**Question**

If sides of triangle are !!17, 25 and 28!!. Then greatest altitude is of length?

!!a)" "15!!

!!b)" "21!!

!!c)" "23!!

!!d)" "!!None

**Solution**

First we need to calculate area of the triangle using Heron's formula.

Semi perimeter = !!(a+b+c)/2!! where !!a,b,c!! are sides of triangle.

!!s = (17+25+28)/2 = 70/2 = 35!!

Now, area of triangle = !!sqrt(s(s-a)(s-b)(s-c)) = sqrt(35(35-17)(35-25)(35-28)) = sqrt(35xx18xx10xx7) = 210!!

We know that altitude of smallest side of triangle is of greatest length.

Area = !!1/2 xx base xx height = 1/2 xx 17 xx h !!

Hence, !!(17h)/2 = 210!!

So, greatest altitude,!!h = 420/17!!