Question

A pole 6m high has a shadow 10 m long when the shadow of a nearby building is 220 m long. How tall is the building? Which ratio is equal to the ratio of the height of the building to its shadow?

Answer 1

Height of the building = 132 m

Ratio of the height of the building to its shadow is, 3 : 5

Explanation:

Answer 2

Height of the building = 132 m

Ratio of the height of the building to its shadow is, 3 : 5 or
`(3)/(5)`

Explanation:

Proportion states that the two ratios or fractions are equal.

As per the statement:

Given: Height of a pole = 6 m , Shadow of a pole = 10 m

and Shadow of a building = 220 m .

Let h be the height of the building.

then, by definition of Proportion;

`(6)/(10) =(h)/(220)`

by cross multiply we have;

`6 * 220 = 10h`

Divide both sides by 10 we get;

`h = (6 * 220)/(10) = 132 m`

Height of the building is, 132 m.

Now to find the ratio of the height of the building to its shadow.

Height of the building to its shadow is written as;

`(Height of the building)/(Shadow of the building)`

Substitute the given values we have;

`(132)/(220)`

Divide both numerator and denominator by 44 we get;

`(3)/(5)` = 3 : 5

Therefore, the ratio of the height of the building to its shadow is, 3 : 5