# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#6

Question

a)   Write  in the form , where c is a positive constant.

A rectangle R has a length of  cm and an area of  cm2.

b)  Calculate the width of R in cm. Express your answer in the form , where p and q are integers to be found.

Solution

a.

Since ;

b.

We are given that the rectangle R has length of  cm and an area of  cm2.

We are required to find the width of the rectangle R.

Expression for the area of the rectangle with length  and width  is;

Therefore;

As demonstrated in (a);

Hence;

If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below.

ü If the denominator is of the form  then multiply both numerator and denominator by

ü If the denominator is of the form  then multiply both numerator and denominator by  .

ü If the denominator is of the form  then multiply both numerator and denominator by  .

We have algebraic formula;