Question

1. Fifteen litres of mixture contain water and milk in the ratio 2:4 . If 3 litres of this mixture are replaced by 3 litres of water, what would be the ratio of water of milk in the new mixture?

2. A telephone booth 210 cm tall cast a shadow 600 cm long. At the sametime, a nearby fire hydrant cast a shadow 240 cm long. Find the height of the fire hydrant.

3. Musa places a mirror on the ground, 5 cm from the base of a tree, He then walks backwards until he can see top of the tree in the mirror. He is now standing 0.75 m from the mirror. Sam's eyes level is 1.75 m high. Label the diagram. Find the height of the tree

Answer 1

1:

If 3 litres are removed from the mixture, 12 litres remain ie (15-3=12)

The 12 litres of mixture contain water and milk in the ratio 2:4

The amount of water in the mixture is $2/(2+4)*12=4 litres$

The amount of milk is $4/(2+4)*12=8litres$

Adding 3 litres of water to the mixture, amount of water becomes $4litres +3litres=7litres$

The new ratio of water to milk becomes $7litres:8litres =7:8$

2:

We will use the triangle similarity theorem because 2 triangles has equal angle between the hypotenuse of the triangle and its lower leg. This angle equal to the height of the sun.

By this theorem: height of telephone Booth/its shadow long =

height of fire hydrant/its shadow long

$\frac{210}{600} = \frac{height \space of \space hydrant}{240}$

$h = 240\times \frac{210}{600} = \frac{50400}{600} = 84 cm$

3:

Let the height of the triangle is x

We know for the similar triangle,

$\Rightarrow \frac{x}{5m}=\frac{1.75m}{0.75}$

$\Rightarrow x=\frac{7}{3}\times 5m$

$\Rightarrow x =\frac{35m}{3}$