*∴*

*l (BP) = l (AP) = y*

**[By perpendicular bisector theorem]**

*As per first condition,*

*y = x + 7*

*∴*

*–*

*x + y = 7 .......eq. no. (1)*

*As per the second condition,*

*Perimeter of ∆ABP = 38*

*∴*

*x + y + y = 38*

*∴*

*x + 2y = 38 ......(2)*

*Adding (1) and (2),*

- x + y = 7 |

x + 2y = 38 |

3y = 45 |

*∴*

*y = 45/3*

*∴*

*y = 15*

*Substituting y = 15 in equation (2)*

*∴*

*x + 2y = 38*

*∴*

*x + 2(15) = 38*

*∴*

*x + 30 = 38*

*∴*

*x = 38 – 30*

*∴*

*x = 8*

*∴*

*l (AB) = 8 cm, l (BP) = l (AP) = 15 cm.*

**The length of sides of ∆**

**ABP are 8 cm, 15 cm and 15 cm.**