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.
well, you didn't say which side is the base, and which are the two equal sides. I will assume A is the vertex between the two equal sides. In that case, AB = AC, so
(A): (4x-3)/15 = (x+3)/5
I assume you can now work out the rest.
If I got the two equal sides wrong, then fix it and devise a similar equation.
Thanks! By the way what is this sort of question called?
To solve this problem, let's start by labeling the sides of the triangle using the given information.
We know that side AB is 4x - 3 over 15, side AC is x + 3 over 5, and side BC is 5x + 6 over 33.
A. Write down an equation for x:
To find the equation for x, we need to use the fact that the triangle is isosceles, which means sides AB and AC are equal. So we can set up an equation:
4x - 3 over 15 = x + 3 over 5
To get rid of the denominators, we can multiply both sides of the equation by the least common multiple (LCM) of 15 and 5, which is 15.
15 * (4x - 3) = 5 * (x + 3)
Now let's simplify the equation:
60x - 45 = 5x + 15
B. Solve the equation:
Next, we need to solve this equation in order to find the value of x.
Let's start by simplifying the equation further:
60x - 5x = 15 + 45
Combining like terms, we have:
55x = 60
To isolate x, we will divide both sides of the equation by 55:
x = 60 / 55
Now, simplifying the right side:
x = 12 / 11
So the value of x is 12 over 11.
C. Work out the length of BC:
To find the length of side BC, substitute the value of x back into the expression for side BC:
BC = 5 * (12 / 11) + 6 over 33
To simplify this expression, we can convert 6 over 33 to an equivalent fraction with a denominator of 11:
BC = 5 * (12 / 11) + (6 / 33) * (3 / 3)
Now we have:
BC = 60 / 11 + 18 / 33
To add these fractions, we need to find a common denominator, which is 33. We can rewrite the first fraction with a denominator of 33:
BC = (60 / 11) * (3 / 3) + 18 / 33
Simplifying further:
BC = (180 / 33) + 18 / 33
Adding the fractions:
BC = 198 / 33
The length of BC is therefore 198 over 33.
To summarize:
A. Equation for x: 4x - 3 over 15 = x + 3 over 5
B. Solve the equation: x = 12 / 11
C. Length of BC: BC = 198 / 33