The sides of a rectangle are in the ratio 2:3. the diagnol is of length 26cm. Find the perimeter.
i havnt got a clue how to do it please help!
The ratio of the sides of the rectangle is represented by:
$\displaystyle \frac{x}{y} = \frac{2}{3}$
The diagonal of a rectangle is found by the Pythagorean Theorem:
$\displaystyle x^2 + y^2 = z^2$
The length of the diagonal is 26. Therefore:
$\displaystyle x^2 + y^2 = (26)^2$
Write everything in terms of one variable (using the ratio given) and then solve for that variable. Once you find one value, you can find the value of the other variable using the ratio.
The perimeter $\displaystyle P = 2x + 2y$