Question

A triangle has sides with lengths: 14, 15, and 7. How do you find the area of the triangle using Heron's formula?

Answer 1

`2sqrt594`

Explanation:

Use Heron's formula

`color(blue)(area=sqrt(s(s-a)(s-b)(s-c))`

Where

`color(orange)((a,bandc)=sides,s=(a+b+c)/2`

So,

`color(purple)(a=14,b=15,c=7,s=(14+15+7)/(2)=36/2=18`

`:.area=sqrt(18(18-14)(18-15)(18-7))`

`rarrsqrt(18(4)(3)(11))`

`rarrsqrt(18(132))`

`rarrsqrt2376`

`rarrsqrt(4*594)`

`color(green)(rArr2sqrt594~~48.7bar5`