What method do I use?!
ABC is an isosceles triangle, these are the lengths of the sides: AB= 4a+3, BC=2b+5, AC= 2a+b The perimeter of the triangle is 32 cm, find the values of a and b. I don't just want the answer I want to know how to get to the answer :)
Answers
Hi Kuromi
22 April 2011
How we can turn that into an equation relating the perimeter with the equations we already have?
22 April 2011
I have no idea...
22 April 2011
AB is one side, along with BC and AC. If we add those together we get the perimeter
22 April 2011
$32 = 4a+3+2b+5+2a+b$
22 April 2011
In other words, 6a+3b+8
22 April 2011
bingo
22 April 2011
So it would be 4a+3+2b+5+2a+b?
22 April 2011
Can you type out that equation?
22 April 2011
22 April 2011
Ah! I get it now! Thank you so much! :)
22 April 2011
Which as you say, can simplify to:
22 April 2011
size*
22 April 2011
We still have 2 unknowns though, however we know that an isosceles triangle has 2 edges the same side
22 April 2011
How do you work out the value of a and b though?
22 April 2011
OOh yeah.
22 April 2011
But, even if we do know the two sides are the same, I don't get how you can find the value of a and b from that? O.o
22 April 2011
Is there any more of the question, because there are several possible answers
22 April 2011
Erm, it is a part b question. The part a question was AB=BC show that 2a-b=1 but I understood that queation.
22 April 2011
Okay, that's useful information. We know that AB=BC. So we know what 2 sides are the same length
22 April 2011
So expand AB=BC into an equation with a's and b's in it.
22 April 2011
erm, so 4a+3=2b+5?
22 April 2011
Exactly!
22 April 2011
Can you rearrange that to find b in terms of a?
22 April 2011
So 4a-2b=5-3?
22 April 2011
almost, we want to keep b on one side of the equation and move all the other terms to the left
22 April 2011
would it be 4a-5+3=2b?
22 April 2011
yes
22 April 2011
then we need to simplify that, and turn 2b into 1b
22 April 2011
or just 'b'
22 April 2011
Divide the whole equation by 2?
22 April 2011
You've got it
22 April 2011
including the numbers which don't have letters?
22 April 2011
so it'll be 2a-1=b
22 April 2011
Precisely
So
becomes
so that
simplifying gives us
and then
22 April 2011
How can we use that with what we figured out earlier?
22 April 2011
Would it be 3(2a-1) instead of 3b?
22 April 2011
Yes! So try writing it out in full
22 April 2011
32=6a+6a-1+8
22 April 2011
which means 32=12a+7
22 April 2011
Not quite, right idea, but be careful multiplying out the brackets on 3(2a-1)
22 April 2011
Ooops, is it 32=6a+6a-3+8?
22 April 2011
Excellent, so to recap: substituting in gives us , expanding the brackets creates
22 April 2011
can you simplify that further and solve what a is?
22 April 2011
32=12a+5
12a=17
a = 1.42 (2 d.p)
22 April 2011
yes! :D
22 April 2011
It can be better to keep it as a fraction until you have solved everything though
22 April 2011
so how do we figure out b?
22 April 2011
Do we do 4a+3, so 4x1.42+3
because 2b+5 equals the same as 4a+3
22 April 2011
Hang on, missed a tiny mistake earlier on
22 April 2011
oops...
22 April 2011
becomes , not
22 April 2011
oh.. which was?
22 April 2011
we both missed that one!
22 April 2011
so
22 April 2011
sneaky mistake?
22 April 2011
, substitute in our value for a: , what does b equal?
22 April 2011
12-5=7
2b=7
b=3.5
22 April 2011
, , ,
22 April 2011
Well done
22 April 2011
How can we check this answer is right?
22 April 2011
Exactly!
22 April 2011
erm by adding it into the equation
32=6a+3b+8
22 April 2011
YES! Thank you so much you've helped me a lot!
22 April 2011
No problem the things to remember are:
Figure out how to turn ALL of the information you have into equations
See what you can rearrange, substitute and simplify
Always work out a way to verify your answer
It never hurts to just play around with the numbers and equations and see where it takes you.
22 April 2011
and always to check afterwards?
22 April 2011
Yes, it's very very easy to make a tiny mistake. Don't be disheartened it's usually easy to fix. That is why showing your workings in exam questions is so important.
22 April 2011
And you too!
22 April 2011
Thank you!
22 April 2011
No problem, have a good Easter
22 April 2011
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