# Math Help - help!!pythogras in trapizium

1. ## help!!pythogras in trapizium

http://www.emaths.co.uk/sats/2009/2009_68_Paper2.pdf < pls go to this link and go question 24 help me solve it plese

2. Originally Posted by coolubi
http://www.emaths.co.uk/sats/2009/2009_68_Paper2.pdf < pls go to this link and go question 24 help me solve it plese
Draw a line parallel to the 20cm side, at the other end, where the kcm side meets the 22cm side, straight down onto the 30cm side.

You now have a rectangle and right-angled triangle.

The sides of this triangle are 22cm, 20cm and (30-k)cm.

To use Pythagoras theorem, the triangle must be right-angled, as this one is.
The sum of the squares of the two shorter sides is the square of the longest side, the hypotenuse.

Then, your formula is $20^2+(30-k)^2=22^2$

$20(20)+(30-k)(30-k)=22(22)$

Multiply this out and write the quadratic equation for k.
K is positive, so find the positive answer for k, when you solve the quadratic, by factorising it after bringing all terms to one side, making it =0,
or using the quadratic formula.