Answer:
40 units.
Step-by-step explanation:
Consider ∆ADC
Perimeter = 26cm (Given)
★ Perimeter of a triangle is the sum of its three sides.
=> AD + DC + AC = 26
Now, from the figure we can see that side AD = DC
Hence we can also write
=> AD + AD + AC = 26
=> 2AD + AC = 26
=> AC = 26 - 2AD ——— ‘1’
Consider ∆ ABC,
Let us consider it's perimeter to be ‘x’.
=> AB + AC + BC = x
Here also we can make out from the figure that side AB = BC
=> AB + AB + AC = x
=> 2AB + AC = x
From ‘1’ substituting AC value, we get
=> 2AB + ( 26 - 2AD ) = x
=> 2AB - 2AD + 26 = x
=> 2( AB - AD ) + 26 = x
=> 2 (7) + 26 = x ( Given )
Therefore perimeter of the ∆ABC (x) = 40
