Question

Solve triangle PQR is PQ 9, PR 7, and QR 8. POR is NOT a right triangle.

Answer 1

Given => PQ = 9 unit
PR = 7 unit
QR = 8 unit

To find => Area of triangle PQR

We can find area of triangle by Heron's Formula.

Where,

s = (9+7+8)/3

= 24/3

= 8

and,
a = 9
b = 7
c = 8

Heron's Formula = $\sqrt{s(s - a)(s - b)(s - c)}$

= $\sqrt{8(8 - 9)(8 - 7)(8 - 8)}$

= $\sqrt{8( - 1)(1)}$

= $\sqrt{ - 8}$

= $2i \sqrt{2}$

Area of triangle = 2i√2 units

Hope this helps!

Answer 2

We will solve this using  Heron's Formula for the area of a triangle.

$\text {Formula = } \sqrt{p(p-a)(p-b)(p-c)} , \text { where p is half the perimeter}$

We will start off by find p:

$\text {p = } \dfrac{9+7+8}{2} = \dfrac{24}{2}= 12$

Now we know, p = 12, we plug in a = 9, b = 8 and c = 7 into the formula to find the area:

$\text {area = } \sqrt{12(12-9)(12-8)(12-7)}$

$\text {area = } \sqrt{12(3)(4)(5)}$

$\text {area = } 26.83 \text{ units}^2$