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.