a, b primes; rectangle area 315 cm^2; find values of a, b in cm

[mcjelski]

Exam revision question. Stumped!

You are given that a and b are prime numbers. The area of the rectangle is 315cm2. Work out the values of a and b in cm.

No matter what i do i cannot find a correct answer.
First time post, sorry if this is in wrong place or I am just being really stupid. Thanks in advance for any help.

 

[mcjelski]

You are given that a and b are prime numbers.
The area of the rectangle is 315cm2.
Work out the value of a and b.

Please help. Cannot find a correct answer and am losing my mind.
Thanks.

 

[stapel]

You are given that a and b are prime numbers. The area of the rectangle is 315cm2. Work out the values of a and b in cm.

How do the primes relate to the rectangle? :shock:

No matter what i do i cannot find a correct answer.

Please reply with a clear listing of your steps for at least one of your attempts. Thank you!

 

[mcjelski]

The previous question involved a rectangle with a diagram marked a=length b=width.
There was no further diagram for the question so I am assuming a and b still represent length and width and that I am looking for 2 prime numbers with a product of 315.
Seriously questioning whether the question is printed correctly but it is from a 2014 uk gcse paper.

 

[Deleted member 4993]

The previous question involved a rectangle with a diagram marked a=length b=width.
There was no further diagram for the question so I am assuming a and b still represent length and width and that I am looking for 2 prime numbers with a product of 315.
Seriously questioning whether the question is printed correctly but it is from a 2014 uk gcse paper.

315 = 7 * 9 * 5

It cannot have only two prime factors.

So there is a mistake in that question!

 

[mcjelski]

Just found the mark scheme for the paper. I agree with the above comment but am posting the question and method/answer from the mark scheme.

If anyone can make any sense of it that would be much appreciated, I'm at a loss but my head is preoccupied with this question and stopping me from moving on.
Thanks

 

[Ishuda]

Just found the mark scheme for the paper. I agree with the above comment but am posting the question and method/answer from the mark scheme.

If anyone can make any sense of it that would be much appreciated, I'm at a loss but my head is preoccupied with this question and stopping me from moving on.
Thanks

Sorry, can't read the image

 

[stapel]

Your first graphic contains what appears maybe to be part of an answer to something else; your second graphic is too tiny for any text to be visible.

The previous question involved a rectangle with a diagram marked a=length b=width.

Ah; well, yes, that's fairly important information.

So you're given that the dimensions of the rectangle from the previous exercise are "a" and "b", where "a" and "b" are prime numbers. You are also given that the area is 315 square units.

The first obvious step, then, would be to note the formula for the area A of a rectangle, given the values of its length L and width W. What formula is that?

To find the prime values for the dimensions, the next obvious step would be to try to factor 315. Since it ends in "5", obviously it is divisible by 5 (which is a prime), so divide. What is the remaining factor? Is this prime?

If not (as has already been noted), then there must be further errors in what has been provided here. Kindly please provide the full and exact text of the exercise and the complete instructions, in a manner which can be viewed. Thank you!

 

[mcjelski]

Sorry. Clearer pic in previous post now. The answer is definitely for the question as it is on official mark scheme for exam paper and find it hard to believe they misprinted it.
Feel ì'm prob missin something simple.

 

[ksdhart2]

Well, I see that this is question 7b. Most of the time, part (b) of a question follows directly from part (a). Perhaps the missing bit of context or information lies there. What does question 7a say?

 

[mcjelski]

Part 7a attatched.

 

[Deleted member 4993]

Part 7a attatched.

Now it becomes a totally different problem!!

L = 3 * a

W = 5 * b

Area of rectangle = L * W = ?? (in terms of a & b)

 

[pka]

@mcjelski , you have caused a number of volunteer helpers to waste a great deal of time: Same on you.
Let this be a lesson to you: Always post a completely defined problem. Don't assume we know what the question is!
\(\displaystyle \begin{align*}(3a)(5b)&=315\\&=3^2\cdot 5\cdot 7\\a\cdot b&=3\cdot 7 \\ \end{align*}\)

Now is the answer not perfectly clear?