Answer:
Length of Jacques' shadow = 1.8 m
Length of flagpole shadow = 4.8 m
Step-by-step explanation:
We are given
Let the length of Jacques' shadow be x and length of flagpole shadow be y
By proportionality theorem
Ratio of height of Jacques to length of Jacques' shadow
=
Ratio of height of flagpole to length of flagpole shadow
Plugging in values
1.5 : x = 4 : y
In fractional form
[tex]\dfrac{1.5}{x} = \dfrac{4}{y}[/tex]
Cross multiply:
[tex]1.5y=x\cdot \:4[/tex]
Divide by 4 both sides:
[tex]\dfrac{1.5y}{4} = x[/tex]
[tex]0.375y =x[/tex]
or
[tex]x = 0.375y[/tex]
or
[tex]x - 0.375y = 0[/tex]
We are given that y - x = 3 m (flagpole shadow has to be > Jacques' shadow)
y-x = 3 can be rearranged as
-x + y = 3
Therefore we get two equations:
x - 0.375y = 0 [1]
-x + y = 3 [2]
Add equations 1 and 2 to eliminate x
x - 0.375y = 0
+
-x + y = 3
----------------
0 + 0.625y = 3
y = 3/0.625
y = 4.8 m
Since x = y - 3 this means x = 48 - 3 = 1.8
Length of Jacques' shadow = 1.8 m
Length of flagpole shadow = 4.8 m