CAIE IGCSE Mathematics Using Pythagoras in Right Triangles

Practise choosing the correct hypotenuse and solving a² + b² = c² for missing sides in right-angled triangles and linked diagrams.

Exam points

write a² + b² = c² with c assigned to the side opposite the right angle
rearrange to c = √(a² + b²) or a = √(c² − b²) according to the missing side
retain sufficient accuracy before using the length in a later perimeter or area calculation

[Maximum number: 5]

Figure for Question C6.1.1 Know and use Pythagoras’ theorem. question 1 — CAIE IGCSE Mathematics Core

NOT TO SCALE

An isosceles triangle has base 12 cm and sides 16 cm. Find the area of this triangle.
$\mathrm{cm}^2$

The height is
$\sqrt{16^2-\left(\frac{12}{2}\right)^2}=\sqrt{220}.$
Hence the area is
$\frac12\times12\times\sqrt{220}=6\sqrt{220}=89.0\ \mathrm{cm^2}\ \text{(approximately)}.$

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C6.1.1 Know and use Pythagoras’ theorem. question 1