8. AB is a segment. The point P is on the perpendicular bisector of segment AB such that length of AP exceeds length of AB by 7 cm. If the perimeter of ∆ABP is 38 cm. Find the sides of ∆ABP.

Solution. Let the length of seg AB be x cm and that of seg AP be y cm




 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.