# pythagoras theorem

• Aug 1st 2005, 02:43 PM
[confused]
pythagoras theorem
a square and a rectangle have the same length diagonal. Find x
square = 2 unknows sides
and the rectangle = 4 by 7 cm
• Aug 1st 2005, 02:47 PM
[confused]
i dont know how to post the diagram... to show all the question. if someone can tell me how to post it, i will.
• Aug 1st 2005, 05:08 PM
MathGuru
the length of the diagonal of any rectangle is:

$\displaystyle \sqrt{(side A)^{2} + (sibe B)^{2}}$

in this case sideA = 4 and sideB = 7.

Can you take it from there?

Hint: Once you know the diagonal you can work backwords to get the length of the side of the square.
• Aug 1st 2005, 06:17 PM
hpe
Quote:

Originally Posted by [confused]
a square and a rectangle have the same lenght diagonal. Find x
square = 2 unknows sides
and the rectangle = 4 by 7 cm

Let x be the unknown side of the square, and let d be the length of the diagonal.

Then by the Theorem of Pythagoras, applied to the square, $\displaystyle x^2 + x^2 = d^2$ or $\displaystyle 2 x^2 = d^2$, and by applying the theorem to the rectangle, $\displaystyle 4^2 + 7^2 = d^2$. You should draw two pictures and label them to convince yourself, one for the square and one for the rectangle. Then explain the pictures to a friend.

Equate the two terms, thus $\displaystyle 2 x^2 = 4^2 + 7^2 = 65$. Therefore, $\displaystyle x^2 = \frac{65}{2}$ and $\displaystyle x = \sqrt{\frac{65}{2}}$.