To find: A function that models area in terms of sides.

Aneeka Hunt

Aneeka Hunt

Answered question

2021-09-24

To find: A function that models area in terms of sides.

Answer & Explanation

okomgcae

okomgcae

Skilled2021-09-25Added 93 answers

The model we want is a function that gives the area of the rectangle.
For the rectangle,
Area=Length×Width
There are two varying quantities: Length and width. Because the function we want dependson its length.
We must express the width in terms of its length x. If we let width of the rectangle by y and perimeter of the rectangle is 20 ft. then we have
2x+2y=20
Subtract 2x from both sides
2y=202x
DIvide by 2,
y=202x2
=10x
The model is the function A that gives the area of the rectangle for any length x.
Area=Length×Width
A(x)=x×(10x)
=10xx2,0<x<10
Thus, the area of the rectangle modeled by the function
A(x)=10xx2,0<x<10.
Final statement:
The area of the rectangle modeled by the function A(x)=10xx2,0<x<10.

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