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

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**Question**

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

A rectangle R has a length of cm and an area of cm^{2}.

**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 cm^{2}.

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;

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