# 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 ðŸ™‚

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

In other words, 6a+3b+8

22 April 2011

$32 = 4a+3+2b+5+2a+b$

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

How do you work out the value of a and b though?

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

size*

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

almost, we want to keep b on one side of the equation and move all the other terms to the left

22 April 2011

So 4a-2b=5-3?

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

becomes , not

22 April 2011

oops...

22 April 2011

oh.. which was?

22 April 2011

we both missed that one!

22 April 2011

sneaky mistake?

22 April 2011

so

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

How can we check this answer is right?

22 April 2011

Well done

22 April 2011

, , ,

22 April 2011

erm by adding it into the equation
32=6a+3b+8

22 April 2011

Exactly!

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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