Question

A boy, who is 5 ft. 6 in. tall, casts a shadow 2 ft long. Find the height of the pole if it casts a shadow 2 yards long.

192 inches

195 inches

198 inches

Answer 1

This is a similar triangles problem:

h/s=H/S

In this case:

p/(2yd(36in/yd))=(5(12)+6)/(2ft(12in/ft))

p/72=66/24, now multiply both sides by 72

p=72(66/24)

p=4752/24

p=198 inches

Answer 2

option C is correct

Height of the pole is, 198 inches

Explanation:

Given: Height of boy = 5ft 6 in , shadow of boy = 2ft

To find the height of pole if it casts a shadow 2 yards long.

Using conversion:

1 yards = 36 inches

1 ft = 12 inches.

Then;

5ft 6 in = 66 inches

2 ft = 24 inches.

2 yards = 72 inches.

Now, using proportions to find the height of pole.

Let height of pole is, h

Proportion says that two ratios are equal.

then;

`(height of boy )/(Shadow of boy) = (Height of pole )/(Shadow of pole)`

Substitute the values:

height of boy = 66 inches , height of pole = h

Shadow of boy = 24 inches and shadow of pole = 72 inches

⇒
`(66)/(24) = (h)/(72)`

Multiply both sides by 72 we get;

`h = (66)/(24) * 72`

or

`h = 66 * 3 = 198 inches`

therefore, the height of the pole is, 198 inches