Question

ABCD is rectangle. Find the length of each diagonal AC=c/3 BD=4-c

Answer 1

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.

Answer 2

The lenght of each diagonals is 1.