Question

The rectangle has an area of 24 square centimeters. find the length a of the rectangle​

Answer 1

Answer : The length of the rectangle (a) is, 8 cm

Step-by-step explanation :

As we are given that,

Area of rectangle = $24cm^2$

Length of rectangle = a

Breadth of rectangle = a - 5

As we know that,

Area of rectangle = Length × Breadth

Now put all the given values in this formula, we get the value of 'a'.

$24cm^2=(a)\times (a-5)$

$24cm^2=a^2-5a$

$a^2-5a-24=0$

By the solving the term 'a', we get the value of 'a'.

a = 8

Thus,

Length of rectangle = a = 8 cm

Breadth of rectangle = a - 5 = 8 - 5 = 3 cm

Therefore, the length of the rectangle (a) is, 8 cm

Answer 2

The length a of the rectangle is 8 cm

Further explanation

To solve the above questions, we need to recall some of the formulas as follows:

Area of Square = (Length of Side)²

Perimeter of Square = 4 × (Length of Side)

Area of Rectangle = Length × Width

Perimeter of Rectangle = 2 × ( Length + Width )

Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Rhombus = 4 × ( Length of Side )

Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )

Let us now tackle the problem !

Given:

Area of Rectangle = A = 24 cm²

Length of Rectangle = L = a cm

Width of Rectangle = W = (a - 5) cm

Unknown:

Length of Rectangle = a = ?

Solution:

This problem is about Area of Rectangle.

$\text{Area of Rectangle} = \text{Length} \times \text{Width}$

$A = L \times W$

$24 = a \times (a - 5)$

$24 = a^2 - 5a$

$a^2 - 5a - 24 = 0$

$(a - 8)(a +3) = 0$

$(a - 8) = 0$

$a = \boxed {8 ~ \text{cm}}$

Learn more

• The perimeter of a polygon : brainly.com/question/6361596
• The perimeter of a rectangle : brainly.com/question/7619923
• The perimeter of a triangle : brainly.com/question/2299951

Answer details

Grade: College

Subject: Mathematics

Chapter: Two Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width