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

The area of the triangle is
`10√(3)`

Explanation:

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

`Area=√(p(p-a)(p-b)(p-c))` , where

• a, b, and c are the length of the three sides of the triangle
• 
  `p=(a+b+c)/(2)`

In Δ XYZ

∵ XZ = 8, YZ = 5, XY = 7

- At first find p

∵
`p=(XY+YZ+XZ)/(2)`

∴
`p=(7+5+8)/(2)=(20)/(2)`

∴ p = 10

∵
`Area=√(p(p-XY)(p-YZ)(p-XZ))`

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

∴
`Area=√(10(10-7)(10-5)(10-8))`

∴
`Area=√(10(3)(5)(2))`

∴
`Area=√(300)`

- Simplify the root

∴
`Area=10√(3)`

The area of the triangle is
`10√(3)`