Marks worth is A 1 B 2 C 2 Please explain next to it though how you got that answer and what to write to get that mark. Clearly explain as I have no clue, don't leave anything out though!
Information needed to solve
There is an isosceles triangle with corners A, B and C. Anyway corner A to B which is a side 4x-3 over 15. Corner A to C x+3 over 5. Corner B to C 5x+6 over 33. These are all on the outside of the triangle. Above is the explanation of the diagram. All lengths are in centimetres.
Questions
A. Write down an equation for x.
B. Solve the equation.
C. Work out the length of BC.
To solve this geometric problem, we can start by using the given information and apply the properties of isosceles triangles. Here's how we can find the answers to the questions step by step:
Step 1: Set up the equation for x based on the given side lengths:
We are given that the lengths of the sides of the triangle are:
AB = (4x - 3) / 15
AC = (x + 3) / 5
BC = (5x + 6) / 33
Since the triangle is isosceles, AB = AC. Setting up an equation using these two side lengths:
(4x - 3) / 15 = (x + 3) / 5
This equation can be solved to find the value of x.
Step 2: Solve the equation for x:
To solve the equation, we can cross-multiply and simplify:
5(4x - 3) = 15(x + 3)
20x - 15 = 15x + 45
20x - 15x = 45 + 15
5x = 60
To isolate x, divide both sides by 5:
x = 12
Now we have determined the value of x.
Step 3: Calculate the length of BC:
Substitute the value of x back into the expression for BC:
BC = (5x + 6) / 33
BC = (5(12) + 6) / 33
BC = (60 + 6) / 33
BC = 66 / 33
BC = 2 cm
Therefore, the length of BC is 2 centimeters.
Summary of answers:
A. The equation for x is (4x - 3) / 15 = (x + 3) / 5.
B. The solution to the equation is x = 12.
C. The length of BC is 2 centimeters.