Question

Searches related to The two sides of a rectangle are x and x + 1. If the length of the diagonal of the rectangle is 5, then what is the area of the rectangle?

Answer 1

✬ Area of Rectangle = 12 m² ✬

Step-by-step explanation:

Given:

• Two sides of rectangle are x and x + 1 .
• Length of diagonal of rectangle is 5 m.

To Find:

• What is the area of rectangle ?

Solution: Let ABCD be a rectangle in which :-

• Length = AB = x
• Breadth = BC = (x + 1 ) m
• Diagonal = AC = 5 m

• We know that the measure of each angle of rectangle is of 90°. So applying Pythagoras Theorem in ∆ABC •

• In ∆ABC → AB (Base) , BC (Perpendicular) and AC (Diagonal)

★ Pythagoras Theorem → Hypotenuse² = Base² + Perpendicular² ★

$\implies{\rm }$ AC² = AB² + BC²

$\implies{\rm }$ 5² = x² + (x + 1)² { By using (a + b)² = a² + 2ab + b² }

$\implies{\rm }$ 25 = x² + (x² + 2x + 1²)

$\implies{\rm }$ 25 = 2x² + 2x + 1

$\implies{\rm }$ 0 = 2x² + 2x + 1 – 25

$\implies{\rm }$ 0 = 2x² + 2x – 24

$\implies{\rm }$ 0 = 2 (x² + x – 12 )

$\implies{\rm }$ 0 = x² + x – 12

$\implies{\rm }$ 0 = x² + 4x – 3x – 12

$\implies{\rm }$ 0 = x ( x + 4 ) – 3 ( x + 4 )

$\implies{\rm }$ 0 = ( x + 4 ) ( x – 3 )

$\implies{\rm }$ x + 4 = 0 , x – 3 = 0

$\implies{\rm }$ x = – 4 , x = 3

Since, x cannot be negative so we will take the value of x = 3

So, The sides are:- Length = x = 3 m and

Breadth = x + 1 = 3 + 1 = 4 m

★ Area of rectangle = Length $\times$ Breadth sq units ★

$\implies{\rm }$ Area = (3 $\times$ 4) m²

$\implies{\rm }$ Area = 12 m²

Hence, The area of rectangle is 12 m².