Question

CHALLENGE PROBLEM!!!

6. To determine the distance across a river, a student uses the sketch and the measurements shown.
Determine the distance across the river. The diagram is not drawn to scale.

Answer 1

The distance across the river is 32 m.

Determining the distance measurement of a figure.

The distance across the river from the figure can be determined by equating the smaller triangle with the overall bigger triangle.

Using the ratio of two similar triangles, Let

• The base of the bigger triangle = 60,
• The base of the smaller triangle = 24
• The height of the higher triangle = 48 + x
• The height of the smaller triangle = x

∴

`(60)/(24)=(48+x)/(x)`

By cross multiplication;

60x = 24(48+x)

60x = 1152 + 24x

60x - 24x = 1152

36x = 1152

x = 1152/36

x = 32

Therefore, the distance across the river is 32 m.