1. The sides of a triangle, in centimetres, are given by 3n-4, 3n+9, 4n+5. Draw a diagram to show the information. If the perimeter of the triangle is 114 cm, find the length of each side.

well, the perimeter is the sum of the sides, so

3n-4 + 3n+9 + 4n+5 = 114
10n = 104

Now it's easy to find n, and then figure the actual side lengths.

To draw a diagram, we need to visualize the triangle with its sides labeled. Let's label the sides as a, b, and c.

Given that the sides are 3n-4, 3n+9, and 4n+5, we can represent them as follows:
Side a = 3n-4
Side b = 3n+9
Side c = 4n+5

Using this information, we can find the values of n, a, b, and c by solving the equation for the perimeter of the triangle.

The perimeter of a triangle is the sum of all its sides. In this case, it is given as 114 cm.

Perimeter = a + b + c
114 = (3n-4) + (3n+9) + (4n+5)

Now, let's solve this equation to find the value of n and the lengths of the sides.

Combine like terms:
114 = 3n + 3n + 4n - 4 + 9 + 5
114 = 10n + 10

Simplify:
10n = 114 - 10
10n = 104

Divide both sides by 10:
n = 10.4

Now, substitute the value of n back into the equations for the side lengths:

a = 3n - 4 = 3(10.4) - 4 = 31.2 - 4 = 27.2 cm
b = 3n + 9 = 3(10.4) + 9 = 31.2 + 9 = 40.2 cm
c = 4n + 5 = 4(10.4) + 5 = 41.6 + 5 = 46.6 cm

Therefore, the length of each side of the triangle is:
Side a = 27.2 cm
Side b = 40.2 cm
Side c = 46.6 cm