a square and a rectangle have the same length diagonal. Find x
square = 2 unknows sides
and the rectangle = 4 by 7 cm
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.
Let x be the unknown side of the square, and let d be the length of the diagonal.Originally Posted by [confused]
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}} $.