Originally Posted by

**sammy28** hi all,

this is a problem that requires the answer expressed as a surd. (calculator not to be used)

The sides of a rectangle are in the ratio 2:3. The diagonal is of length 26cm. Find the perimeter.

The answer given in the answer section is $\displaystyle 20\sqrt13$

$\displaystyle 26^2 = 626$

sides are therefore

$\displaystyle \sqrt{\frac{2}{5} * 626} \mbox{ and} \sqrt{\frac{3}{5} * 626}$

and perimeter

$\displaystyle 2\sqrt{\frac{1352}{5}} + 2\sqrt{\frac{2028}{5}}$

using prime factors of 1352 and 2028

$\displaystyle 26\sqrt{\frac{8}{5}} + 52\sqrt{\frac{3}{5}}$

using a calculator the answer i calculated is not equal to the textbooks answer