Answer:
Recall the following result:
In a rectangle ABCD, the diagonals AC and BD are equal to each other, that is, AC = BD.
Consider the following statement:
[tex]\text{AC}=\frac{c}{3}[/tex] and BD =4-c
The objective is to find the length of each diagonal.
As per the result:
In a rectangle ABCD:
AC = BD
Substitute the given values:
[tex]\frac{c}{3} =4-c[/tex]
Multiply both sides by 3:
[tex]c = 3(4-c)[/tex]
Simplify:
c = 12-3c
Add 3c to both sides :
4c= 12
Divide both sides by 4;
c = 3
Then,
[tex]\text{AC}=\frac{3}{3}=1[/tex]
BD=4-3 = 1
Therefore, the length of each diagonal is, 1.
