Question

In △XYZ , XZ=8 , YZ=5 , and XY=7 . What is the area of the triangle? Enter your answer, in simplified radical form, in the box.

Answer 1

Answer:

The area of the triangle is $10\sqrt{3}$

Step-by-step explanation:

Let us use Heron's Formula for the area of a triangle

$Area=\sqrt{p(p-a)(p-b)(p-c)}$ , where

• a, b, and c are the length of the three sides of the triangle
• $p=\frac{a+b+c}{2}$

In Δ XYZ

∵ XZ = 8, YZ = 5, XY = 7

- At first find p

∵ $p=\frac{XY+YZ+XZ}{2}$

∴ $p=\frac{7+5+8}{2}=\frac{20}{2}$

∴ p = 10

∵ $Area=\sqrt{p(p-XY)(p-YZ)(p-XZ)}$

- Substitute the values of p, XY, YZ, and XZ in the rule above

∴ $Area=\sqrt{10(10-7)(10-5)(10-8)}$

∴ $Area=\sqrt{10(3)(5)(2)}$

∴ $Area=\sqrt{300}$

- Simplify the root

∴ $Area=10\sqrt{3}$

The area of the triangle is $10\sqrt{3}$