Respuesta :
The dimensions of the base of the pyramid are width: 5/2cm and length: 8.5cm.
What is a pyramid?
A three-dimensional shape is a pyramid. Its base is a flat polygon. The other faces, referred to as lateral faces, are all triangles.
The number of sides on its base is equal to the number of lateral faces.
The volume of a pyramid?
The volume of a pyramid is 1/3 base area × height.
What is a Quadratic equation?
A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Here, we have
volume of a pyramid = 90cm
Length = (2x+1)
Width = x
Perpendicular height = 18cm
Then by the volume of a pyramid, we get
Area of the base = (2x + 1)x = (2x² +x) (cm²)
Volume of the pyramid = 1/3×(2x² +x)×18 = 90
= 12x² + 6x = 90
= 2x² + x - 15 = 0
= (2x-5)(x+3)
x = 5/2
Length=3(5/2)+1
Length=7.5+1
Length=8.5cm
Hence, the dimensions of the base of the pyramid are: Width 5/2cm ; Length 8.5cm.
To learn more about the volume of a pyramid from the given link
https://brainly.com/question/29021848
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