Use this information to write down an equation involving $x$ and $y$.

Use this ratio to write down $y$ in terms of $x$.

Find the value of $x$ and of $y$.

${x^2} + {y^2} = {68^2}$ (or 4624 or equivalent)     (A1)     (C1)

[1 mark]

$\frac{y}{x} = \frac{3}{4}$     (M1)

Note:     Award (M1) for a correct equation.

$y = \frac{3}{4}x{\text{ }}(y = 0.75x)$     (A1)     (C2)

[2 marks]

${x^2} + {\left( {\frac{3}{4}x} \right)^2} = {68^2}{\text{ }}\left( {{\text{or }}{x^2} + \frac{9}{{16}}{x^2} = 4624{\text{ or equivalent}}} \right)$     (M1)

Note:     Award (M1) for correct substitution of their expression for $y$ into their answer to part (a). Accept correct substitution of $x$ in terms of $y$.

$x = 54.4{\text{ (cm), }}y = 40.8{\text{ (cm)}}$     (A1)(ft)(A1)(ft)     (C3)

Note:     Follow through from parts (a) and (b) as long as $x > 0$ and $y > 0$.

[3 marks]