Question

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

Answer 1

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


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

We will start off by find p:


`\text {p = } (9+7+8)/(2) = (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 = } √(12(12-9)(12-8)(12-7))`


`\text {area = } √(12(3)(4)(5))`


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

Answer 2

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 =
`√(s(s - a)(s - b)(s - c))`

=
`√(8(8 - 9)(8 - 7)(8 - 8))`

=
`√(8( - 1)(1))`

=
`√( - 8)`

=
`2i √(2)`

Area of triangle = 2i√2 units

Hope this helps!