Question

When the width of a rectangle with a length of 3/5 foot was decreased by 1/3 foot, the area of the rectangle became 7/25. Find the original width of the rectangle.

Answer 1

The original width is 4/5

Explanation:

To find this, note that the new dimensions of the rectangle and 3/5 (lengths) and x - 1/3 (width), in which x is the original width. Now we multiply them together and set equal to 7/25

3/5(x - 1/3) = 7/25

3/5x - 1/5 = 7/25

3/5x = 12/25

x = 4/5

Answer 2

`\large\boxed{\text{The original width}\ =(4)/(5)\ ft}`

Explanation:

`\text{The dimensions of rectangle:}\ (3)/(5)* w.\\\\\text{The dimensions of new rectangel:}\ (3)/(5)*\left(w-(1)/(3)\right)\\\\\text{The area of the new rectangle:}\ A=(7)/(25)\ ft^2\\\\\text{We have the equation:}\\\\(3)/(5)\left(w-(1)/(3)\right)=(7)/(25)\qquad\text{multiply both sides by 25}\\\\25\!\!\!\!\!\diagup^5\cdot(3)/(5\!\!\!\!\diagup_1)\left(w-(1)/(3)\right)=25\!\!\!\!\!\diagup^1\cdot(7)/(25\!\!\!\!\!\diagup_1)`

`15\left(w-(1)/(3)\right)=7\qquad\text{use the distributive property}\\\\15w-15\!\!\!\!\!\diagup^5\cdot(1)/(3\!\!\!\!\diagup_1)=7\\\\15w-5=7\qquad\text{add 5 to both sides}\\\\15w=12\qquad\text{divide both sides by 15}\\\\w=(12:3)/(15:3)\\\\w=(4)/(5)`