The perpendicular bisector of side ab of ∆abc intersects side bc at point d. find ab if the perimeter of ∆abc is with 12 cm larger than the perimeter of ∆acd.

The required length of is .

Step-by-step explanation:

Given: The perpendicular bisector of side of intersects side at point and the perimeter of  .

From the figure,

        .......(1)              (as is perpendicular bisector of side )

Now, In and

                                          ( from equation 1 )

                              ( Both )

                                        ( Common side)

                             ( by SAS congruence rule)

         .........(2)                   (by CPCT)

As per question,

The perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.

Hence, the length of is .

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Hence, AB=12.

Step-by-step explanation:

We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.

this means that side AE=BE.

Also we could clear;ly observe that

ΔBED≅ΔAED

( since AE=BE, side ED common, ∠BED=∠AED

so by SAS congruency the two triangles are congruent)

Now we are given that:

the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.

i.e. AB+AC+BC=AC+AD+CD+12

AB+BC=AD+CD+12

as AD=BD

this means that AD+CD=BD+CD=BC

AB+BC=BC+12

AB=12

Hence AB=12

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-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0