Question

A length of the side of triangle which are 13,x and y if xy =105 then perimeter of triangle is

Answer 1

Perimeter of triangle is 35.

Step-by-step explanation:

Perimeter of triangle = sum of all the sides = 13 + x + y

condition to form a triangle is that,

sum of any two sides ≥ remaining side

so,    

13 + x ≥ y

13 + y ≥ x

x + y ≥ 13

Given that x×y = 105

105 can be written as the product of two number as 15×7 or 21×5 or 35×3.

so possible set of (x,y) are (15,7) , (21,5) , (35,3)

putting all set of x and y in the following conditions

13 + x ≥ y

13 + y ≥ x

x + y ≥ 13

only x=15 and y=7 is satisfying.

so perimeter = 13 + 15 + 7 = 35.

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