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.
[tex]\text{Area of Rectangle} = \text{Length} \times \text{Width}[/tex]
[tex]A = L \times W[/tex]
[tex]24 = a \times (a - 5)[/tex]
[tex]24 = a^2 - 5a[/tex]
[tex]a^2 - 5a - 24 = 0[/tex]
[tex](a - 8)(a +3) = 0[/tex]
[tex](a - 8) = 0[/tex]
[tex]a = \boxed {8 ~ \text{cm}}[/tex]
Learn more
- The perimeter of a polygon : https://brainly.com/question/6361596
- The perimeter of a rectangle : https://brainly.com/question/7619923
- The perimeter of a triangle : https://brainly.com/question/2299951
Answer details
Grade: College
Subject: Mathematics
Chapter: Two Dimensional Figures
Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width
