Question

A rectangular piece of cardboard with an L-shaped hole is held 1.0m directly in front of a point source of light. The cardboard is 1.5m away from a wall. The cardboard and the wall are parallel. The height H of the L is 15.40cm. The width W of the L is 7.08cm.

How tall is the image of the L on the wall?
How wide is the image of the L on the wall?

Answer 1

The first thing we will do is to project the beam of light from the point source to the board and then to the wall. This is going to generate relationships right triangles with each other.
to understand a little this observe the following image:

so as you can see all the information you give us exercise.
Yellow rays projection causes us about similar triangles in relation to the height H of the L, and the green rays of projection causes us about similar triangles in relation to the width W of L

the next thing we will do is work case by case basis for the values of H' and W'

for H '

defining variables thus

H = 15.40cm

d = 1.0m = 100cm

D =  1.5m = 150cm

the first thing you will find is the value of θ using trigonometry

  

and now with this value of θ we will use the same trigonometric function for the largest triangle and determine H '

and now to W '

defining variables thus

W =  7.08cm

d = 1.0m = 100cm

D =  1.5m = 150cm

the first thing you will find is the value of θ using trigonometry

and now with this value of θ we will use the same trigonometric function for the largest triangle and determine W'