word problem question

rectangle abcd has a perimeter of 24 wides ab and dc are twice as long as sides ad bc calculate the length of side ac

Answers
its kinda level 5 work
scardashit
13 May 2012
First, you need to make the problem into an algebraic formula. So, you have your rectangle and you know that the long sides are twice as long as the short sides. So, the rectangle is made up of 2 sides which you can label x (the short sides) and 2 sides you can label as 2x (the long sides, because they are twice the length of the short sides).
joannarodwell
13 May 2012
If you add up all the x's you get x + x + 2x + 2x = 6x
joannarodwell
13 May 2012
So, now you have: x + x + 2x + 2x
joannarodwell
13 May 2012
Then, you need to work out x by dividing both sides by 6. If you do that you get to x = 4
joannarodwell
13 May 2012
You know the perimeter is 24 so you can put that into the equation too: 6x = 24
joannarodwell
13 May 2012
So, now, by plugging in the x values you can work out the length of each side. So, the short sides are 4 and the long sides are 8.
joannarodwell
13 May 2012
Now, to work out ac (the diagonal) you need to use pythagoras (a^2 + b^2 = c^2). So, you need to do 4^2 + 8^2 = ?
joannarodwell
13 May 2012
Therefore... 16+64 = 80
joannarodwell
13 May 2012
So... 4^2 = 16 and 8^2 = 64
joannarodwell
13 May 2012
And if you do that, the answer you should get is 8.94 :)
joannarodwell
13 May 2012
Then you need to work out the square route of 80 (c^2) to get the length of ac
joannarodwell
13 May 2012
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