2012 Year 9 &10 Mathematics Marathon (5 Viewers)

[enoilgam]

I don't get anything after the word perimeter.

Its basically asking you to think of a semi circle whose area equals its perimeter. They then want you to prove that the radius of such a shape equals the result shown in the question.

 

[Demento1]

Someone paraphrase question 8 because i don't get what it's trying to ask lmao

Interpreted: A semi-circle has the area equal to the perimeter. Prove that the radius of this circle is equal to the expression below.

Let 'r' be radius and form an equation.

 

[Fawun]

Its basically asking you to think of a semi circle whose area equals its perimeter. They then want you to prove that the radius of such a shape equals the result shown in the question.

So long story short, it's asking me to prove that the area of a semi circle is equal to its perimeter? ok

 

[Demento1]

Q9 is a very good question, it doesnt require any mechanical interaction at all.
Think Pythagorean Triads.

lol it's a wonderful thing.

 

[enoilgam]

So long story short, it's asking me to prove that the area of a semi circle is equal to its perimeter? ok

No - its asking you to think of a particular semi-circle which happens to have its perimeter equal to its area. Then you want to prove that the radius of that shape equals the result shown.

 

[Fawun]

Someone tell me if i'm on the right track

So far I have:

1/2 x pi x r^2 (half the area of a circle) = pi x r + 2r (perimeter of a semi circle including the base which is the diameter)

inb4imalreadywrong

 

[enoilgam]

Someone tell me if i'm on the right track

So far I have:

1/2 x pi x r^2 (half the area of a circle) = pi x r + 2r (perimeter of a semi circle including the base which is the diameter)

inb4imalreadywrong

Keep going.

 

[HSC2014]

For Q9, is it saying that the base is 1m longer than one of the equal sides, or the sum of both equal sides?

 

[Fawun]

Wait so now i have to make r the subject? since it's looking for the radius?

 

[enoilgam]

For Q9, is it saying that the base is 1m longer than one of the equal sides, or the sum of both equal sides?

I was unsure of this as well - to make matters more interesting, the school did not hand out solutions

Wait so now i have to make r the subject? since it's looking for the radius?

Yes, keep going.

 

[Fawun]

I can't

i'm stuckkk

EDIT: So far now, I have pi*r^2 = 2pi*r + 4r

 

[Sy123]

For Q9, is it saying that the base is 1m longer than one of the equal sides, or the sum of both equal sides?

One of the equal sides, not the sum of them. If this were the case then the lengths of the sides are not integers (think of a famous Pythagorean triad)

 

[Demento1]

For Q9, is it saying that the base is 1m longer than one of the equal sides, or the sum of both equal sides?

My interpretation: Let 'x' be equal side of the isosceles triangle. Let 'x+1' be the base of the triangle.

 

[HSC2014]

My interpretation: Let 'x' be equal side of the isosceles triangle. Let 'x+1' be the base of the triangle.

Yeah I've been messing around with that for a while now. I WILL GET THE ANSWER WAIT FOR IT LOL. Sy123 has pointed out some famous pythag triad I am unaware of, so I'm not going to google it

 

[enoilgam]

My interpretation: Let 'x' be equal side of the isosceles triangle. Let 'x+1' be the base of the triangle.

This is how I interpreted it - I just wanted to make sure (overall, this paper is a bit unlear in areas).

 

[Timske]

I can't

i'm stuckkk

EDIT: So far now, I have pi*r^2 = 2pi*r + 4r

Factorise something

 

[enoilgam]

I can't

i'm stuckkk

EDIT: So far now, I have pi*r^2 = 2pi*r + 4r

Factorise.

 

[Fawun]

am i doing it right someone confirm pls










????

 

[enoilgam]

I can probably guarantee you that you have seen these set of numbers before.

Nice.

 

[Fawun]

do i square root it