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Avery is designing a large rectangular sign. They want the sign to have an area of $2\,\text{m}^2$ and a width of $\frac{4}{5}\,\text{m}$ . How tall should the sign be?

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Area and perimeter: word problems

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Q. Avery is designing a large rectangular sign. They want the sign to have an area of

2\,\text{m}^2

and a width of

\frac{4}{5}\,\text{m}

. How tall should the sign be?

Define height: Let $h$ be the height of the rectangular sign. $\newline$ We know that the area of a rectangle is given by the formula $\text{Area} = \text{width} \times \text{height}$ .
Calculate area: Area of the rectangular sign: $2\,\text{m}^2$ $\newline$ Width of the rectangular sign: $\frac{4}{5}\,\text{m}$ $\newline$ Substitute the known values into the area formula to find the height. $\newline$ $2 = \left(\frac{4}{5}\right) \cdot h$
Find height using area formula: Solve for $h$ by dividing both sides of the equation by $\frac{4}{5}$ . $\frac{2}{\left(\frac{4}{5}\right)} = \frac{\left(\frac{4}{5}\right) \cdot h}{\left(\frac{4}{5}\right)}$ $2 \cdot \left(\frac{5}{4}\right) = h$ $2.5 = h$
Solve for height: Calculate the height. $\newline$ $2 \times \left(\frac{5}{4}\right) = 2.5$ $\newline$ Height of the rectangular sign: $2.5$ m

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