Question

The lengths of the sides of a triangle are (2a+1) cm, (3a+2) cm and (4a-1) cm, for what value of 'a' is the perimeter of the triangle 92 cm???



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Answer 1

SOLUTION :-

• First Side of Triangle = (2a + 1) cm.

• Second Side of Triangle = (3a + 2) cm.

• Third Side of Triangle = (4a – 1) cm.

Perimeter of the Triangle = 92cm.

According to the Question,

Sum of All Sides = Perimeter of Triangle.

➙ 1st Side + 2nd Side + 3rd Side = Perimeter.

➙ 2a + 1 + 3a + 2 + 4a – 1 = 92.

➙ 9a + 2 = 92.

➙ 9a = 92 – 2.

➙ 9a = 90.

➙ a = 90 ÷ 9.

➙ a = 10 cm.

Therefore,Value of a = 10cm.

Sides of Triangle :-

• First Side = 2a + 1 = 21 cm.

• Second Side = 3a + 2 = 32 cm.

• Third Side = 4a – 1 = 39 cm.

VERIFICATION :-

➙ 1st Side + 2nd Side + 3rd Side = Perimeter.

➙ 21 + 32 + 39 = 92 cm.

➙ 60 + 32 = 92 cm.

➙ 92 = 92 cm.

LHS = RHS.

Hence, Verified.