Question

the dimensions of a rectangular garden are 5ft (length) by 3ft (width) the owner wants to increase the lenght by twice as much as the width increases to attain an area of 36 sq ft. set up an equation of a quadratic formula to solve for the new dimensions if this garden

Answer 1

Let the new length be \(L\) and the new width be \(W\). Since the owner wants to increase the length by twice as much as the width, you can express the new length in terms of the current width:

\[ L = 3 + 2W \]

The area of the rectangular garden is the product of length and width:

\[ LW = 36 \]

Now, substitute the expression for \(L\) into the area equation:

\[ (3 + 2W) \cdot W = 36 \]

Simplify and rearrange the equation to form a quadratic equation:

\[ 2W^2 + 3W - 30 = 0 \]

This is a quadratic equation in the form \(ax^2 + bx + c = 0\), where \(a = 2\), \(b = 3\), and \(c = -30\).