# Sara used 34 meters of fencing to enclose a rectangular region. To be sure that the region was a rectangle, she measured the diagonals and found that they were 13 meters each. What are the length and width of the rectangle?

##### 1 Answer

**Length(L) #= 4# meters**

**Width(W) #= 13# meters**

#### Explanation:

**Given:**

Sara used **fencing to enclose a rectangular region.**

Hence,

**Perimeter of a rectangle** as shown below is

Hence **2x(Length + Width) = 34** meters

Let us assume that **Length = L meters** and **Width = W meters.**

So,

What is below is a **rough sketch and NOT drawn to scale**

Hence,

AB = CD = L meters

AC = BD = W meters

We are given that **Diagonals are 13 meters long**

We know that,

the **diagonals of a rectangle** are **equal length;**

**diagonals of a rectangle also bisect each other**

What is below is a **rough sketch and NOT drawn to scale**

Angle

Using Pythagoras Theorem, we can write

Add

Taking square root on both sides

We consider only positive values

Substitute

Using the identity

Hence,

Hence, **width of the rectangle = **

We already have

Substitute the value of

Add

**Length of the rectangle = 4** meters

Substitute the values of

to verify our results

We get

Hence, our rectangle has

**Length(L) #= 4# meters**

**Width(W) #= 13# meters**