Question

A triangle has side lengths of (5.3p+ 7.6) centimeters, (3.8p – 4.3) centimeters,

and (2.4q - 7.4) centimeters. Which expression represents the perimeter, in

centimeters, of the triangle?

Answer 1

The perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres

Explanation:

Let a, b and c be the sides off a triangle. Its perimeter P = a + b + c.

Now, the triangle has side lengths (5.3p+ 7.6) centimetres, (3.8p – 4.3) centimetres, and (2.4q - 7.4) centimetres.

Let a = (5.3p+ 7.6) cm , b = (3.8p – 4.3) cm and c = (2.4q - 7.4) cm

So the perimeter of the triangle is P = a + b + c

substituting the values of a, b and c, we have

P = (5.3p + 7.6) cm + (3.8p – 4.3) cm + (2.4q - 7.4) cm

opening the brackets and collecting like terms, we have

P = (5.3p + 3.8p + 2.4q + 7.6 - 4.3 - 7.4) cm

P = (9.1p + 2.4q - 4.1) centimetres

So the perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres