Answer :
Final answer:
To find the dimensions of the rectangular dog pen, we can use algebraic expressions and solve a quadratic equation. the correct answer is: b. Quadratic equations.
Explanation:
To find the dimensions of the rectangular dog pen, we can use algebraic expressions. Let's assume the width of the pen is 'w' feet. According to the problem, the length must be 'w + 2' feet. We can now set up an equation to find the area of the pen: w * (w + 2) = 72. This equation represents the length times the width equals the area of 72 square feet. Expanding the equation, we get w^2 + 2w = 72. Rearranging the terms, we have the quadratic equation w^2 + 2w - 72 = 0. Solving this quadratic equation will help us find the dimensions of the pen. Since this problem involves finding the dimensions of the pen, the correct answer is: b. Quadratic equations. The question asks for using algebraic expressions and quadratic equations to determine the dimensions of a dog pen given its area and the fact that its length is a fixed number of feet longer than its width, which requires solving for width first and then length.
The question involves using algebraic expressions and quadratic equations to determine the dimensions of a rectangular dog pen given its area and the relationship between its length and width. When given the area of a rectangle, A, and the expression that the length, L, is 'feet longer than the width, W', we can write the equation A = W(L). If, for example, L is 3 feet longer than W, then the equation becomes A = W(W + 3) which is a quadratic equation. By solving this quadratic equation, one can find the dimensions of the rectangle. We can also apply proportions and scales when comparing areas or creating scale drawings. Using a measuring tape may be necessary for actual measurements of spaces. Additionally, units conversions are essential, for instance, converting yards to feet or inches, as indicated in various example problems. In a scenario where we need to scale down a rectangular fish pond, a unit scale ratio is used to determine the dimensions of the scale model. For instance, a pond that is 10 feet by 20 feet with a scale of 1/2 in = 5 ft would require calculating the dimensions by dividing the real dimensions by the scale factor.
