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.
To draw a diagram of the triangle, we can label the sides as follows:
Side 1: 3n - 4 cm
Side 2: 3n + 9 cm
Side 3: 4n + 5 cm
To find the length of each side, we need to solve the equation:
Side 1 + Side 2 + Side 3 = Perimeter
Substituting the given values:
(3n - 4) + (3n + 9) + (4n + 5) = 114
Simplifying:
10n + 10 = 114
Subtracting 10 from both sides:
10n = 104
Dividing both sides by 10:
n = 10.4
Now, substituting the value of n back into the expressions for the sides:
Side 1: 3(10.4) - 4 = 31.2 - 4 = 27.2 cm
Side 2: 3(10.4) + 9 = 31.2 + 9 = 40.2 cm
Side 3: 4(10.4) + 5 = 41.6 + 5 = 46.6 cm
Therefore, the length of each side of the triangle is:
Side 1: 27.2 cm
Side 2: 40.2 cm
Side 3: 46.6 cm
To draw a diagram for this problem, you'll need to represent each side of the triangle using their respective expressions:
Let's assume the first side is represented by "a" (3n-4), the second side is represented by "b" (3n+9), and the third side is represented by "c" (4n+5).
So, the diagram would consist of a triangle with labeled sides "a," "b," and "c".
Now, let's move on to finding the length of each side given that the perimeter of the triangle is 114 cm.
The perimeter of a triangle is the sum of the lengths of its three sides. In this case, we have:
a + b + c = 114
Substituting the expressions for each side:
(3n-4) + (3n+9) + (4n+5) = 114
Now, let's solve this equation:
Group the like terms:
(3n + 3n + 4n) + (-4 + 9 + 5) = 114
Combine like terms:
10n + 10 = 114
Subtract 10 from both sides:
10n = 104
Divide by 10:
n = 10.4
Now that we have the value of n, we can substitute it back into the expressions to find the length of each side:
a = 3n - 4 = 3(10.4) - 4 = 26.8
b = 3n + 9 = 3(10.4) + 9 = 39.2
c = 4n + 5 = 4(10.4) + 5 = 49.6
Therefore, the lengths of the sides of the triangle are approximately:
a ≈ 26.8 cm
b ≈ 39.2 cm
c ≈ 49.6 cm