CAIE IGCSE Mathematics Extended E4.4.2 Use the Relationships Between Lengths and Areas of Similar Shapes and Questions

Practise Extended CAIE IGCSE Mathematics by relating corresponding lengths and areas through similarity scale factors.

Exam points

Use the scale factor for lengths and the square of the scale factor for areas in similar shapes.
Calculate missing lengths or areas from corresponding similar figures.
Explain proportional relationships between corresponding sides and areas.

[Maximum number: 3]

Figure for Question CAIE IGCSE Mathematics Extended E4.4.2 Use the Relationships Between Lengths and Areas of Similar Shapes and Questions question 1 — CAIE IGCSE Mathematics Extended

NOT TO
SCALE

The two shapes are mathematically similar.
The area of the larger shape is $36 \mathrm{~cm}^{2}$ and the area of the smaller shape is $25 \mathrm{~cm}^{2}$ .
The height of the larger shape is 9 cm and the height of the smaller shape is $x \mathrm{~cm}$ .

Find the value of x.

$\frac{15}{2}$ oe

M2 for $\frac9x=\frac65$ oe, or $x^2=\frac{25}{36}\times9^2$ oe or better.
M1 for $\sqrt{\frac{36}{25}}$ or $\sqrt{\frac{25}{36}}$ oe or better, or for $\left(\frac9x\right)^2=\frac{36}{25}$ or $\left(\frac{x}{9}\right)^2=\frac{25}{36}$ oe or better.

All question bank results loaded

CAIE IGCSE Mathematics Extended E4.4.2 Use the Relationships Between Lengths and Areas of Similar Shapes and Questions question 1