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.

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

Answer:

option C is correct

Height of the pole is, 198 inches

Step-by-step 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;

$\frac{height of boy }{Shadow of boy} = \frac{Height of pole }{Shadow of pole}$

Substitute the values:

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

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

⇒  $\frac{66}{24} = \frac{h}{72}$

Multiply both sides by 72 we get;

$h = \frac{66}{24} \times 72$

or

$h = 66 \times 3 = 198 inches$

therefore, the height of the pole is, 198 inches