Question

How do you solve the triangle given `trianglePQR, p=12, q=16, r=20`?

Answer 1

18.97 (2.d.p)

Explanation:

As we are given 3 sides of the triangle, with no right angle, we can use Heron's formula to solve for the area. Heron's formula can be used when we know the 3 sides of a triangle, which in this case we know `p, q and r`.

Heron's formula: `A = sqrt(s-(s-a)(s-b)(s-c)`

where s = `(a+b+c)/2` (half perimeter of the triangle)

In this case, we can assume `a, b and c = p, q and r` respectively.

So, `s=(12+16+20)/2`
= 24

Now, we just plug the numbers into Heron's formula to get the area of the triangle.

A = `sqrt(24-(24-12)(24-16)(24-20)`
= 18.97 (rounded to two decimal places)