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 problem, we'll use the information provided about the isosceles triangle and the lengths of its sides. Let's go through each question step-by-step:
A. Write down an equation for x:
We can start by setting up a proportion using the side lengths of the triangle. The ratio of the lengths of side AB to AC is equal to the ratio of the expressions given:
(4x - 3) / 15 = (x + 3) / 5
B. Solve the equation:
To solve this equation, we'll cross-multiply. Multiply the 15 by (x + 3), and multiply the 5 by (4x - 3):
15(x + 3) = 5(4x - 3)
Expanding both sides of the equation:
15x + 45 = 20x - 15
To isolate x, we need to get all the terms with x on one side and the constant terms on the other side. We can do this by subtracting 15x from both sides and adding 15 to both sides:
15x - 20x = -15 - 45
-5x = -60
Now, divide both sides by -5 to solve for x:
(-5x) / (-5) = (-60) / (-5)
x = 12
C. Work out the length of BC:
Using the value of x we found in question B, substitute it into the expression for side BC:
BC = 5x + 6
BC = 5(12) + 6
BC = 60 + 6
BC = 66
So, the length of BC is 66 centimeters.
In summary:
A. The equation for x is (4x - 3) / 15 = (x + 3) / 5.
B. By solving the equation, we found that x = 12.
C. The length of BC is 66 centimeters.