Maclaurin 2019 Q2

Let the sides of the triangle adjacent to the right angle be \(a\) cm and \(b\) cm. Since the area is 150 cm² we have \(300 = ab\).

The length of the hypotenuse, in cm, is \(60 - (a + b)\), so that, using Pythagoras’ theorem, we have

After expanding and simplifying, we get

and so, substituting \(300 = ab\), we obtain \(a + b = 35\). It follows that \(a\) and \(b\) are roots of the equation \(x^2 - 35x + 300 = 0\), which we may factorise as \((x - 20)(x - 15) = 0\). Therefore \(a\) and \(b\) are 15 and 20, in either order.

Hence the sides of the triangle have lengths 15 cm, 20 cm and 25 cm.