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:
\(\text{AC}=\frac{c}{3}\) 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:
\(\frac{c}{3} =4-c\)
Multiply both sides by 3:
\(c = 3(4-c)\)
Simplify:
c = 12-3c
Add 3c to both sides :
4c= 12
Divide both sides by 4;
c = 3
Then,
\(\text{AC}=\frac{3}{3}=1\)
BD=4-3 = 1
Therefore, the length of each diagonal is, 1.
