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If bar(XY) = 3, what is the area of Delt...

If `bar(XY) = 3`, what is the area of `Delta XYZ` ?

A

`1.949`

B

`3.074`

C

`5.324`

D

`7.529`

Text Solution

Verified by Experts

The correct Answer is:
B
Drop an altitude, and you'll reveal two hidden special right triangles :

Now you can use the known side ratios of 45-45-90 and 30-60-90 triangles to get all the lengths you need. If the hypotenuse of a 30-60-90 is 3, then the shorter leg is `(3)/(2)` and the longer leg is `(3sqrt(3))/(2)` :

Now that you know one of the 45-45-90, you know the length of the other leg.

Now you have the base and the height . The base is `(3sqrt(3)+3)/(2)`, and the height is `(3)/(2)`. Thus,
Area of triangle `=(1)/(2)` (base)(height)
`=((1)/(2))((3sqrt(3)+3)/(2))((3)/(2))`
`=(3(3sqrt(3)+3))/(8)=(9sqrt(3)+9)/(8)`
`~~3.074`
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