Question

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directions: use the drawing tool(s) to form the correct answer on the provided grid. use the formulas for the area and perimeter of a rectangle to solve this problem. draw a rectangle that has: an area of 35 square centimeters a perimeter of 24 centimeters the point on the grid represents one vertex of this rectangle. draw the sides of the rectangle along the grid lines. each square in the grid has a side length of 1 centimeter.

Explanation:

Step1: Recall rectangle formulas

Let the length of the rectangle be $l$ and the width be $w$. The area formula is $A = lw$ and the perimeter formula is $P=2(l + w)$. We know that $A = 35$ and $P = 24$. So we have the system of equations

$$\begin{cases}lw=35\\2(l + w)=24\end{cases}$$

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Step2: Simplify perimeter equation

From $2(l + w)=24$, divide both sides by 2 to get $l + w=12$, which means $l = 12 - w$.

Step3: Substitute into area equation

Substitute $l = 12 - w$ into $lw = 35$, we get $(12 - w)w=35$. Expand to $12w-w^{2}=35$, or $w^{2}-12w + 35=0$.

Step4: Solve quadratic equation

Factor the quadratic equation $w^{2}-12w + 35=0$ as $(w - 5)(w - 7)=0$. So $w=5$ or $w = 7$. If $w = 5$, then $l=7$; if $w = 7$, then $l = 5$.

Answer:

Draw a rectangle with length 7 grid - squares and width 5 grid - squares starting from the given vertex along the grid lines.