Question

The area of a rectangular garden is given by the quadratic function: A (x) = -6x^2 + 105x– 294

Answer 1

Answer:

Bree is correct

Step-by-step explanation:

Given

Area of rectangle;

$A (x) = -6x^2 + 105x - 294$

Joe's Result:

$Length = -6x + 21\\Width = x - 4$

Bree' Result

$Length = -3x + 42\\Width = 2x - 7$

Required

Determine whose result is correct and why.

To determine the correct result, we simply find the roots of the quadratic function

$A (x) = -6x^2 + 105x - 294$

Such that A(x) = 0

$-6x^2 + 105x - 294 = 0$

Start Factorization;

Expand

$A (x) = -6x^2 + 105x - 294$

Group the above expression in 2s

$A(x) = (-6x^2 + 84x) + (21x - 294)$

Factorize

$A(x) =2x(-3x + 42) -7 (-3x + 42)$

$A(x) = (2x - 7)(-3x + 42)$

Recall that; Area of a rectangle is calculated by;

$A(x) = Length * Width$

By comparison;

$Length = 2x - 7\\Width = -3x + 42$

At this point, we can conclude that Bree's computation is correct;

Reason

The product of (-3x + 42) and (2x – 7) will result in the given area of the rectangle