Question

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

Answer 1

The lenght of each diagonals is 1.

Answer 2

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}=(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:

`(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}=(3)/(3)=1`

BD=4-3 = 1

Therefore, the length of each diagonal is, 1.