Triangle XYZ is a right triangle with altitude YA . If XA=11 and AZ=7 determine XY

Question

a. 3√22

b.√77

c.3√14

d.√170

c is not the answer

Answer 1

Hi Somalia,

 

Here's the solution you need to use the geometric mean theorem. This theorem tells us that:

 

YA = sqrt(XA*AZ) = sqrt(11*7) = sqrt(77)

 

XY is the hypotenuse of the right triangle XAY, and with XA = 11 and YA = sqrt 77, we can use the Pythagorean theorem to find XY. 

 

XY = sqrt(11² + (sqrt 77)² = sqrt(121+77) = sqrt(198) = 3sqrt(22), which is answer a.