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In △XYZ , XZ​=7 , YZ=7 , and XY=6 .

What is the area of the triangle?

Enter your answer, in simplified radical form, in the box.

 Apr 14, 2020
 #1
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This is an isosceles triangle.

Drop a perpendicular from Z to side XY; call the point of intersection P.

Since the triangle is isosceles, P will be the midpoint of side XY.

 

Consider triangle(XZP).

It is a right triangle.

Its hypotenuse is 7, one of its sides is 3.

Using the Pythagorean Theorem to find the other side:  32 + ZP2  =  72 

   --->   9 + ZP2  =  49   --->   ZP2  =  40   --->   ZP  =  sqrt(40)   --->   ZP  =  2 · sqrt(10)

 

The base of the triangle is XY; the height is ZP.

Its area is  ½ · 6 · 2 sqrt(10)  =  6 · sqrt(10)

 Apr 14, 2020

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