**Ques - x varies directly as (y² +z²). At y = 1 and z = 2, the value of x is 15. Find the value of z, when x = 39 and y = 2.**

**(a) 2**

**(b) 3**

**(c) 4**

**(d) 6**

**Solution - **

x varies directly as y² +z²

= x ∝ y² +z²

Remove the sign of proportional and and a constent k.

Therefore,

**x = k****(y² +z²)**** ** ___________ (1)

Now,

Put the value of x, y, z in eq. 1.

x = k(y² +z²)

15 = k(1² +2²)

15 = 5k

**k = 3**

Again,

Put the value of k = 3, x = 39 and y = 2 in eq. 1.

x = k(y² +z²)

39 = 3(2² + z²)

39 = 3(4 + z²)

39 = 12 + 3z²

39 - 12 = 3z²

27 = 3z²

z² = 27/3

z² = 9

**z = 3**

Hence,

The correct answer is option** (b) 3.**

Thank You