Question

AB is given.point p lies in the perpendicular bisector of AB such that the measure AP is double than AB. If the perimeter of triangle ABPis 35cm. Find the measure of side of ABP

Answer 1

∴  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.