Question

A 12-centimeter rod is held between a flashlight and a wall as shown. Find the length of the shadow on

the wall of the rod is 45 cm from the wall and 15 cm from the light.

Answer 1

Answer:

48 cm

Step-by-step explanation:

Given:

Distance of rod from the wall = 45 cm

Distance of rod from the light = 15 cm

Length of rod = 12 cm

We can see that <DAM and <BAF are equal

Also, <DMA and <BFM are equal because they are corresponding angles

To find the length of the shadow, let's take the equation

$\frac{DM}{BF} = \frac{AM}{A.F}$

Where.:

DM = ½ of length of the rod = ½*12 = 6

A.F = 15 + 45 = 60 cm

AM = 15 cm

Therefore,

$\frac{DM}{BF} = \frac{AM}{A.F}$

$= \frac{6}{BF} = \frac{15}{60}$

Cross multiplying, we have:

15 * B.F = 60 * 6

15 * B.F = 360

$BF = \frac{360}{15}$

BF = 24 cm

The shadow on the wall =

2 * BF

= 2 * 24

= 48 cm

The shadow on the wall is 48 cm