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
[tex] \frac{DM}{BF} = \frac{AM}{A.F} [/tex]
Where.:
DM = ½ of length of the rod = ½*12 = 6
A.F = 15 + 45 = 60 cm
AM = 15 cm
Therefore,
[tex] \frac{DM}{BF} = \frac{AM}{A.F} [/tex]
[tex]= \frac{6}{BF} = \frac{15}{60} [/tex]
Cross multiplying, we have:
15 * B.F = 60 * 6
15 * B.F = 360
[tex]BF = \frac{360}{15}[/tex]
BF = 24 cm
The shadow on the wall =
2 * BF
= 2 * 24
= 48 cm
The shadow on the wall is 48 cm
