Question

2)

Question 2 Using the following figure, find z. y X 3 12 a) 03/5 b) O 15 06 d) 06/5 e) None of the above

Answer 1

Solution-

To find the caluevof z, let us first marked the points on triangle as A, B , C and D as shown in figure below-

~ 니 n z .

Now,

In ∆ABC, <A =90°.So, by Pythagoras theoram we get

y² + z² = (13 +2)²

Or y² + z² = 15² ...(1)

In ∆ABD, <D = 90°. So, by Pythagoras theoram we get

y² = x² + 3² .....(2)

Similarly

In ∆ACD, <D = 90°. So, by Pythagoras theoram we get

z² = x² + 12² .....(3)

Now, adding equations (1) and (3) and substracting them from equation (2) to get

(y² + z²) + (z²) - (y²) = (15² ) + (x² +12²) -(x² + 3²)

Or y² +z² + z² - y² = 225 + x² + 144 - x² -9

Or 2z² +0 = 360 +0

Or z² = 360/2

Or z² = 180

Or z = √(180)

Or z = 6√5

Hence, z = 6√5 (option-d)