Question

If the area of a rectangle is 10in^2, the length (2+sqrt(2))in. What is the width?

Answer 1

Area=length times width
area=10
length=2+√2
width=w

10=(2+√2)(w)
divide both sides by (2+√2)
$\frac{10}{2+ \sqrt{2} } =w$
if we were to rationalize the dnomenator
multiply by$\frac{2- \sqrt{2} }{2- \sqrt{2} }$
$\frac{10(2- \sqrt{2})}{4-2 } =w$
$\frac{20- 10\sqrt{2}}{2} =w$
$10- 5\sqrt{2} =w$

the width is 10-5√2 m