Question

the function f x =x2 +3x-10 models the area of a rectangle. a: describe the length and width of the rectangle in terms of x b: what is a rectangle in terms of x

Answer 1

A .
`Length = x+5\\breadth = x-2`

B. domain of
`f(x)= x^2+3x-10` here is all values of x > 2 .

Explanation:

Correct question is : the function
`f(x)= x^2+3x-10`models the area of a rectangle. a: describe the length and width of the rectangle in terms of x b: what is a domain for above function in relation to rectangle . Let's solve:

a: describe the length and width of the rectangle in terms of x

Let's factorise
`f(x)= x^2+3x-10` :

⇒
`f(x)= x^2+5x-2x-10`

⇒
`f(x)= x(x+5)-2(x+5)`

⇒
`f(x)= (x+5)(x-2)`

Since , ⇒
`f(x)=length(breadth)` So

`Length = x+5\\breadth = x-2` .

b: what is a domain for above function in relation to rectangle

Since area is always > 0 , and (length , breadth)>0 So,

⇒
`f(x)= (x+5)(x-2)>0\\x>0 \\x>2` Therefore, domain of
`f(x)= x^2+3x-10` here is all values of x > 2 .