Answer :
Answer:
3.75 feet.
Step-by-step explanation:
Given:
Two people are standing next to each other on horizontal ground.
One is 5 feet tall, and the other is 6 feet tall.
The shadow of the person who is 6 feet tall is 3 feet shorter than twice the length of the shadow of the person who is 5 feet tall.
Question asked:
How long is the shorter person’s shadow?
Solution:
Let the shadow 5 feet person = [tex]x[/tex]
As given, shadow of 6 feet person is 3 feet shorter than twice the length of the shadow of 5 feet person.
Then, the shadow 6 feet person = [tex]2x-3[/tex]
Now, as we know:
Ratio of the shadow of two objects are in proportion of their heights, so:-
[tex]\frac{Shadow\ of\ 5\ feet \ person}{Shadow\ of\ 6\ feet\ person}=\frac{5}{6}[/tex]
=[tex]\frac{x}{2x-3} =\frac{5}{6}[/tex]
By cross multiplication:
[tex]6\times x=5\times(2x-3)\\\\6x=10x-15[/tex]
Subtracting both sides by [tex]10x[/tex]
[tex]6x-10x=10x-10x-15\\-4x=-15\\[/tex]
Adding both sides by minus
[tex]4x=15[/tex]
Dividing both sides by 4
[tex]x=\frac{15}{4}[/tex]
[tex]x=3.75\ feet[/tex]
shadow 5 feet person = [tex]x[/tex] = 3.75 feet
Therefore, shadow of the shorter person is 3.75 feet.
