Maths help please: Pythagoras/algebra

[Laura Corin]

'A rectangle has a diagonal of 12cm and its long sides are twice the length of its short sides. What are the lengths of the sides of the rectangle?'

Calvin gets as far as:

H squared = x squared + y squared
144 = x squared + (2x)squared

But he can't get to the number with algebra. He tried various values to check whether x was a whole number, and it's not. The answer is 5.37 and 10.73, but how does he get to it? My algebra is more than rusty...

Thank you

Laura

[8FillTheHeart]

I'm not sure why he isn't getting the correct answer. (though I am not sure why he used a y)

s=short side
2s=long side

B/c a^2+b^2=c^2
s^2 + (2s)^2= 144
s^2+ 4s^2=144
5s^2=144
s^2=28.8
square root both sides and s= 5.37

(Only thing I can think of is that he didn't square his 2???)

[Linda in TX]

Everything you have so far is correct.
144= x squared + (2x) squared.

Now (2x) squared is 4(x squared), so we now have

144 = x squared + 4 x squared
144 = 5 x squared
144/5 = x squared
12/ (square root of 5) = x

I don't have my calculato, but that will be less than 12/2 so the answer of 5.37 seems reasonable.

Linda

[Valerie(TX)]

He was on the right track. :) See below.

'A rectangle has a diagonal of 12cm and its long sides are twice the length of its short sides. What are the lengths of the sides of the rectangle?'

Calvin gets as far as:

H squared = x squared + y squared
144 = x squared + (2x)squared

He's got it started correctly, just needs to continue:

144= x^2 + (2x)^2
144= x^2 + 4x^2 (or 4 x squared) 2x times 2x = 4x^2
144= 5x^2 Add x squared plus 4x squared
144 divided by 5 = x^2
5.37 (rounded) = x
10.73 = 2x = y




But he can't get to the number with algebra. He tried various values to check whether x was a whole number, and it's not. The answer is 5.37 and 10.73, but how does he get to it? My algebra is more than rusty...

Thank you

Laura

[Laura Corin]

I'm not sure why he isn't getting the correct answer. (though I am not sure why he used a y)


The theorem is written out with x and y in his book, so those were the letters he used.

Thanks again

Laura

[Laura Corin]

Where would this problem come in the US maths sequence? Algebra 1 or before that?

Thanks again,

Laura

[Pamela H in Texas]

yes, Algebra I

[lgm]

Where would this problem come in the US maths sequence? Algebra 1 or before that?

Thanks again,

Laura


It's considered Pre-Algebra in NY and taught in 7th grade for both honors and on-grade level.

http://www.glencoe.com/sites/common_assets/workbooks/math/Pre-AlgebraOK/papw.pdf

or

http://phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefix=adk&wcsuffix=0099

[Valerie(TX)]

Where would this problem come in the US maths sequence? Algebra 1 or before that?

Thanks again,

Laura

It has come up in our pre-algebra text, and then in *every* level after that. :)

[Laura Corin]

It has come up in our pre-algebra text, and then in *every* level after that. :)

This text would be used by pupils aged (depending on ability/school) between about age 12 and 14 in the UK.

Laura