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.

Answers

Answer 1

Answer:

Answer:

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

Step-by-step explanation:

$\text{The dimensions of rectangle:}\ (3)/(5)* w.\n\n\text{The dimensions of new rectangel:}\ (3)/(5)*\left(w-(1)/(3)\right)\n\n\text{The area of the new rectangle:}\ A=(7)/(25)\ ft^2\n\n\text{We have the equation:}\n\n(3)/(5)\left(w-(1)/(3)\right)=(7)/(25)\qquad\text{multiply both sides by 25}\n\n25\!\!\!\!\!\diagup^5\cdot(3)/(5\!\!\!\!\diagup_1)\left(w-(1)/(3)\right)=25\!\!\!\!\!\diagup^1\cdot(7)/(25\!\!\!\!\!\diagup_1)$

$15\left(w-(1)/(3)\right)=7\qquad\text{use the distributive property}\n\n15w-15\!\!\!\!\!\diagup^5\cdot(1)/(3\!\!\!\!\diagup_1)=7\n\n15w-5=7\qquad\text{add 5 to both sides}\n\n15w=12\qquad\text{divide both sides by 15}\n\nw=(12:3)/(15:3)\n\nw=(4)/(5)$

Answer 2

Answer:

Answer:

The original width is 4/5

Step-by-step 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

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