Simultaneous Equations Structured Questions | Cambridge O Level Additional Mathematics

Question 1 of 3 · 10 marks

Simultaneous Equations · 1 - Applied Non-Linear Modeling & Enclosure Optimization

4 parts

Additional Mathematics 4037 · Question 1Paper 2 · Calculator[10 marks]

A farmer constructs a rectangular enclosure $ABCD$ divided into two identical rectangular pens by an internal fence parallel to side $AB$ , as shown in the diagram. The total length of fencing used for all outer boundaries and the internal fence is $120\,\text{m}$ . The total enclosed area of the two pens combined is $450\,\text{m}^2$ . Let $x\,\text{m}$ be the width $AB$ and $y\,\text{m}$ be the depth $AD$ .

(a)

Write down two simultaneous equations in $x$ and $y$ representing the total fencing length and the total enclosed area.

[2]

(b)

Show that $x$ satisfies the quadratic equation $3x^2 - 120x + 900 = 0$ .

[3]

(c)

Solve the equation to determine the two possible sets of dimensions $(x, y)$ for the enclosure.

[3]

(d)

The farmer specifies that the width $x$ must be strictly greater than the depth $y$ . State the required dimensions of the enclosure and calculate the area of a single pen.

[2]