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WAEC Mathematics 2013 Paper

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Question : 36

Total: 48

in the diagram, the height of a flagpole |TF| and the length of its shadow |FL| re in the ratio 6:8. Using k as a constant of proportionality, find the shortest distance between T and L

7K units
10K units
12K units
14k units

Solution:

Concept:

The flagpole and its shadow form a right-angled triangle, so use Pythagoras' theorem.

Explanation:

Given ratio

|TF| : |FL| = 6 : 8

and constant of proportionality

k

,

height

|TF| = 6k

and shadow

|FL| = 8k

.

The shortest distance between

T

and

L

is the hypotenuse

|TL|

.

By Pythagoras:

|TL|^2 = (6k)^2 + (8k)^2

.

So

|TL|^2 = 36k^2 + 64k^2 = 100k^2

.

Thus

|TL| = \sqrt{100k^2} = 10k

.

Answer:

10k

units, i.e. Option B.

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