Pythagoras' theorem

A right-angled triangle $ABC$ is drawn. $AB=1.6$ m and $BC=2.8$ m.

Feb/March 2018

A right-angled triangle is shown in the diagram. It has a side of 8.5 cm, a base of 10.8 cm, and the figure is marked NOT TO SCALE.

Feb/March 2020

The diagram represents a right-angled triangle. Its vertical side measures 8.5 cm and its base measures 10.8 cm. NOT TO SCALE.

Feb/March 2020

The figure shows two right-angled triangles, $ABC$ and $ACD$. For triangle $ABC$, $AB=39\text{ cm}$ and $BC=52\text{ cm}$. For triangle $ACD$, $CD=25\text{ cm}$. The side $AD$ is marked as $x$ cm. The figure is not drawn to scale.

Feb/March 2023

Find what $x$ is.

May/June 2015

Write the mathematical name beneath each triangle shown.

May/June 2015

The diagram depicts a rectangular field, $ABCD$, together with a straight path, $BD$. Here $BD = 93.5\text{ m}$ and $BC = 82.5\text{ m}$.

May/June 2016

The figure depicts a rectangular playground $ABCD$ (NOT TO SCALE). $AB = 23.4\text{ m}$ and $AC = 35.1\text{ m}$.

May/June 2018

A right-angled triangle $ABC$ is displayed. $AB = 2.5\text{ cm}$ and $BC = 4.1\text{ cm}$. The right angle lies at $B$. The diagram is labelled NOT TO SCALE.

May/June 2018

The diagram shows a triangle with two equal sides of $5\,\text{cm}$, a base measuring $4\,\text{cm}$, and a perpendicular height $h$ dropped from the top vertex to the base.

May/June 2022

Calculate the length of $AB$.

May/June 2023

A right-angled triangle ABC and a semicircle are shown. The semicircle has radius $4.5$ cm. Also, $AC = 8.9$ cm and $BC = 13.2$ cm.

May/June 2023

Calculate the length of $AB$.

May/June 2023

Calculate $AB$.

May/June 2024

In the diagram, triangle $ABC$ is right-angled. $AB = 52.5\text{ cm}$ and $AC = 59.5\text{ cm}$. The right angle is at $B$. The figure is marked NOT TO SCALE.

May/June 2025

A right‑angled triangle is shown. One side measures 35 cm and another side measures 22 cm. The hypotenuse has been marked as $h$ cm. The diagram is marked NOT TO SCALE.

May/June 2025

A right-angled triangle is drawn with one side $5\text{ cm}$, the hypotenuse measures $8\text{ cm}$ and the base is $x\text{ cm}$. The diagram is marked NOT TO SCALE.

Oct/Nov 2015

A right-angled triangle is drawn. One side measures 18 cm, the base measures 26 cm, and the hypotenuse is marked $x$ cm. The diagram is labelled NOT TO SCALE.

Oct/Nov 2015

A right-angled triangle is drawn here, and it is not to scale. One vertical side measures $5\text{ cm}$, the hypotenuse measures $8\text{ cm}$, and the base is labelled $x\text{ cm}$.

Oct/Nov 2015

The figure depicts a right-angled triangle $ABC$, with $AB = 8$ cm, $AC = 18$ cm, and the right angle at $B$.

Oct/Nov 2017

The figure is a right-angled triangle. Its vertical side measures 3.9 cm, the hypotenuse measures 8.5 cm, and the base is marked $x$ cm. The figure is not drawn to scale.

Oct/Nov 2019

The diagram depicts a right-angled triangle. The horizontal side measures 31 cm, the vertical side measures 28 cm, and the hypotenuse is $x$ cm.

Oct/Nov 2019

One side of a rectangle has length 12 cm, and its diagonal has length 13 cm.

Oct/Nov 2020

Calculate the value of $PQ$.

Oct/Nov 2020

One side of a rectangle measures 12 cm. Its diagonal measures 13 cm.

Oct/Nov 2020

Triangle $ABC$ is illustrated. The length of $AB$ is $6\text{ cm}$. From $C$, a perpendicular is drawn to the line containing $AB$ and meets it at right angles, with the height labelled $h\text{ cm}$. The diagram is not drawn to scale.

Oct/Nov 2020

A right-angled triangle is illustrated. The hypotenuse measures $14\text{ cm}$, the base is $10\text{ cm}$ and the perpendicular side is $h\text{ cm}$. NOT TO SCALE.

Oct/Nov 2022

A right-angled triangle is drawn in the diagram. Its base measures 10 cm, the hypotenuse measures 14 cm, and the vertical side is marked $h$ cm. The figure is labelled NOT TO SCALE.

Oct/Nov 2022

Calculate the area enclosed by triangle $ABC$.

Oct/Nov 2023

Find the height of the triangle.

Oct/Nov 2025

The diagram depicts a box shaped as a cuboid with side lengths 5 cm, 5 cm and 7 cm. Mala has a straight rod measuring 10 cm.

Oct/Nov 2025