Respuesta :
The length of the rectangle is 3 cm
Applications of Quadratic equations
From the question, we are to determine the value of the length of the rectangle
To find the length of the rectangle, we will determine the value of x in the given equation
The given equation is
[tex]x^{2} + 5x =24[/tex]
This can be written as
[tex]x^{2} +5x -24 =0[/tex]
Factorizing
[tex]x^{2} +8x - 3x -24 = 0 [/tex]
[tex]x(x+8) -3(x+8)=0[/tex]
[tex](x-3)(x+8)=0[/tex]
Then,
[tex]x-3 = 0[/tex] OR [tex]x + 8 = 0[/tex]
x = 3 OR x = -8
Since, the length of the rectangle cannot be negative, the value of x is 3.
Hence, the length of the rectangle is 3 cm.
Learn more on solving quadratic equations here: https://brainly.com/question/8649555
