Can any Maths Geniuses help out?

[convert]

Can any Cleva maths bunnies help out with this question please. My Daughter got this as a Mock GCSE question, and I'm fooked If I can work it. And I studied Maths at "A" level about 300 yrs ago.

I attach a PDF of the question, anyone know how to work this out? I know it must use the Perpendicular height (unknown "h") or they wouldn't use it. I don't know.... a number of times I thought I had it, but I can't prove it.

My son sussed it BUT he's done maths "A" level last year and is doing further maths "A" level this year starting a Maths degree at Uni in September...

He's the wrong one to ask because he's on another planet when it comes to maths, me and my daughter just looked at each other when he went off on one. His way (what ever it was he tried to explain) Can't be the way to do it because my daughter doesn't have a clue what he's talking about and it's too deep for a GCSE student. It's not what they are looking for.

Anyone have a simple explanation?

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[nara]

If you know know that the overall height of the triangle ABD is h,you can divide it into smaller triangles and use Pythagorus' theorum to work out areas. A bit of algebra plus arithmetic should get you on from there, but my brain's too sore at the moment to go into more detail.

There may be a simpler way, but I did maths in the Dark Ages.

 

[Trabbs]

As nara says, the area of the ABC triangle can be calculated by forming two right angle triangles by dropping a line from A to a point between B and C (call it E). These two areas can be calculated as can the area of triangle ACD by calculating the area of the triangle formed by the line from A to E and then deducting the area of the small triangle AEC formed by the new line. You will see that the area of ABC is larger than ACD by twice the size of the triangle AEC. Hope this helps.

 

[geofden]

Area of a triangle is 1/2 x base x height
Therefore area of triangle ABC is 1/2 x BC x h
similarly area of triangle ACD is 1/2 x CD x h
Divide one by the other and cancel out the common items, i.e. 1/2 and h and hey presto!

Need a beer now my brain hurts!

:Cheers:

 

[Tawke]

Area of a triangle is 1/2 x base x height
Therefore area of triangle ABC is 1/2 x BC x h
similarly area of triangle ACD is 1/2 x CD x h
Divide one by the other and cancel out the common items, i.e. 1/2 and h and hey presto!

Need a beer now my brain hurts!

:Cheers:

Isn't 1/2 x base x height for right angled triangles?

 

[geofden]

No it works for all triangles

http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i9/bk7_9i5.htm

 

[Novac]

Thanks for the maths link

Shame I am too junior in status to download the pdf and have a crack at the geometry problem. But thanks for the Plymouth Project link I will have a good nose through that later.

 

[davidh]

Shame I am too junior in status to download the pdf and have a crack at the geometry problem. But thanks for the Plymouth Project link I will have a good nose through that later.

here u go knock ur self out
i think it means fook all lol

 

[langland]

Area of a triangle is 1/2 x base x height
Therefore area of triangle ABC is 1/2 x BC x h
similarly area of triangle ACD is 1/2 x CD x h
Divide one by the other and cancel out the common items, i.e. 1/2 and h and hey presto!

Need a beer now my brain hurts!

:Cheers:

A perfect and simple explanation

 

[convert]

Geofden, thanks, me thinks this is what they are after..

The whole paper can be downloaded from the edexcel web site and many others in case you need an excuse for another beer :Clap:

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[convert]

Stop press...

Just showed my son, he immdiately said no that's not right, because because sin 90 is one and as it's not a right angle it's sin blah blah blah... lost me... can't remember.

Then he twigged they aren't asking for numeric vaues, just why the formula is right.

So he sort of went off muttering something under his breath.

Ha !

Then looked at what my daughter had done BEFORE getting him involved, and she got it right, but he insisted she got it wrong which started all this off.

So much for our in house mathematician eh?

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