# Math Help - surds

1. ## surds

Two rectangles have equal area.

The length of the first is (root2-10) and the width is the same.

The second rectangle has width root3.

Find the length of the second rectangle. Give the answer is the form p(root3).

I tried:

calling the unknown side x...

(root10 - 2) (root10 - 2) = root3 (x)

10 - 4root10 + 4 = root3 (x)

...but can't see how to find answer. Help!

PS how do I show square root using latex?

2. Combine the like terms on the left-hand side, and then divide through by the square root of three.

3. got as far as...

14 - 4root30 = x
---------------
3

....not sure from here

4. What is it?
is it $\sqrt{2}-10$ or $\sqrt{10}-2$?

here is the link you need: http://www.mathhelpforum.com/math-he...-tutorial.html

Two rectangles have equal area.

The length of the first is (root2-10) and the width is the same.

The second rectangle has width root3.

Find the length of the second rectangle. Give the answer is the form p(root3).

I tried:

calling the unknown side x...

(root10 - 2) (root10 - 2) = root3 (x)

10 - 4root10 + 4 = root3 (x)

...but can't see how to find answer. Help!

PS how do I show square root using latex?
$A_1 = (\sqrt{2}-10)^2 = 102-20\sqrt{2}$

$A_2 = A_1 = x\sqrt{3}$

$\therefore 102-20\sqrt{2} = x\sqrt{3}$

$x = \frac{102-20\sqrt2}{\sqrt3} = \frac{102\sqrt3-20\sqrt6}{3}$

I multiplied both sides by $\frac{\sqrt{3}}{\sqrt3}$ in order to give a rational denominator as this is the convention

6. Originally Posted by BabyMilo
What is it?
is it $\sqrt{2}-10$ or $\sqrt{10}-2$?

here is the link you need: http://www.mathhelpforum.com/math-he...-tutorial.html

sorry!
it's $(\sqrt10 - 2)$ for each side of the first rectangle

7. $(\sqrt10 -2) (\sqrt10 - 2) = \sqrt3 (x)$

$10 -4\sqrt10 + 4 = \sqrt3 (x)$

$14 - 4\sqrt10 = \sqrt3 (x)$

$\frac{14 - 4\sqrt10}{\sqrt3} = x$

multiplying the left by \sqrt3 to rationalise the surd fraction gives this:

$\frac{14 - 4\sqrt10\sqrt3}{3} = x$

...not sure from here