### The two sides of a rectangle are *x* and *x* + 1. If the length of the diagonal of the rectangle is 5 cm, then what is the area of the rectangle?

*x*

*x*+ 1

**Answer:**

12 cm^{2}

**Step by Step Explanation:**

- Given the two sides and diagonal of the rectangle ABCD are
,*x*and*x*+ 1**5**respectively, as shown below:

Let**A**be the area of the the rectangle ABCD.

Area of the rectangle ABCD (A)

= (*x*)(*x*+ 1)

=*x*^{2}+*x* - In triangle ABC, by using
**Pythagoras Theorem**we get,

(*x*)^{2}+ (*x*+ 1)^{2}= (5)^{2}

⇒*x*^{2}+*x*^{2}+ 2*x*+ 1 = 25

⇒ 2*x*^{2}+ 2*x*+ 1 = 25

⇒ 2*x*^{2}+ 2*x*+ 1 - 25 = 0

⇒ 2*x*^{2}+ 2*x*- 24 = 0

⇒ 2(*x*^{2}+*x*- 12) = 0

⇒*x*^{2}+*x*- 12 = 0

⇒ 1x^{2}+ 4x - 3x -12 = 0

⇒ x(1x + 4) - 3(1x + 4) = 0

⇒ (1x + 4)(x - 3) = 0

**either,**1x + 4 = 0| **or,**x - 3 = 0⇒ x = -4/1 | ⇒ x = 3

The value of**x**can not be negative. So the value of**x**is 3. - Now, the area of the rectangle ABCD =
*x*^{2}+*x*

=*(3)*^{2}+*(3)*

= 12 - Therefore, the area of the rectangle is
**12**.