Question

In ∆ ABC the length of side BC is greater than the length of side AB by 3 cm but is less than the length of side AC by 2cm .If the perimeter of the triangle is 53cm .find the length of the greatest side of ∆ ABC.

Answer 1

Answer:

20

Step-by-step explanation:

BC is greater than AB but less than AC, so AC is the greatest side.  This is the one we want.  Let x be this length (i.e. the length of AC).

Since BC is less than AC by 2, the length of BC is x-2.

Since BC is greater than AB by 3, the side AB is 3 less than BC, so AB has length (x-2)-3 = x-5.

The perimeter is the sum of all three side lengths, which is then

x + (x-2) + (x-5) = 3x - 7.

We're told the perimeter is 53 though, so

3x - 7 = 53

=>  3x = 60

=>  x = 20.