Answer:
The area of the triangle is [tex]10\sqrt{3}[/tex]
Step-by-step explanation:
Let us use Heron's Formula for the area of a triangle
[tex]Area=\sqrt{p(p-a)(p-b)(p-c)}[/tex] , where
- a, b, and c are the length of the three sides of the triangle
- [tex]p=\frac{a+b+c}{2}[/tex]
In Δ XYZ
∵ XZ = 8, YZ = 5, XY = 7
- At first find p
∵ [tex]p=\frac{XY+YZ+XZ}{2}[/tex]
∴ [tex]p=\frac{7+5+8}{2}=\frac{20}{2}[/tex]
∴ p = 10
∵ [tex]Area=\sqrt{p(p-XY)(p-YZ)(p-XZ)}[/tex]
- Substitute the values of p, XY, YZ, and XZ in the rule above
∴ [tex]Area=\sqrt{10(10-7)(10-5)(10-8)}[/tex]
∴ [tex]Area=\sqrt{10(3)(5)(2)}[/tex]
∴ [tex]Area=\sqrt{300}[/tex]
- Simplify the root
∴ [tex]Area=10\sqrt{3}[/tex]
The area of the triangle is [tex]10\sqrt{3}[/tex]
