The longest side of a triangle is a cm.                                                                                    (3)The second side is b cm shorter than the first side.The third side is half as long as the second side.Write an expression, in its simplest form, for the perimeter ofthe triangle. Show your working.

The longest side of the triangle is a cm.

The second side is b cm shorter than the first side, so it is a - b cm.

The third side is half as long as the second side, so it is (a - b)/2 cm.

The perimeter of a triangle is the sum of the lengths of all its sides. Therefore, the perimeter P of this triangle is:

P = a + (a - b) + (a - b)/2

To simplify this expression, we first need to add the like terms:

P = 2a - b + (a - b)/2

Then, we can simplify the fraction by multiplying the numerator and the denominator by 2:

P = 2a - b + 2(a - b)/4

This simplifies to:

P = 2a - b + (a - b)/2

So, the simplest form for the perimeter of the triangle is:

P = 2.5a - 1.5b

The longest side of the triangle is a cm.

The second side is b cm shorter than the first side, so it is a - b cm.

The third side is half as long as the second side, so it is (a - b)/2 cm.

The perimeter of a triangle is the sum of the lengths of all its sides. Therefore, the perimeter of this triangle is:

a + (a - b) + (a - b)/2

To simplify this expression, we first need to add the a's together and then subtract the b's:

2a - b + (a - b)/2

This simplifies to:

2.5a - 1.5b

So, the perimeter of the triangle, in its simplest form, is 2.5a - 1.5b cm.