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Nisha likes to make small rectangular paintings of cats. One of her paintings has an area of $33\,\text{cm}^2$ and a width of $7 \frac{1}{2}\,\text{cm}$ . What is the height of this painting?

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Area and perimeter: word problems

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Q. Nisha likes to make small rectangular paintings of cats. One of her paintings has an area of

33\,\text{cm}^2

and a width of

7 \frac{1}{2}\,\text{cm}

. What is the height of this painting?

Understand relationship: Understand the relationship between area, width, and height in a rectangle. $\newline$ The area $A$ of a rectangle is the product of its width $W$ and height $H$ . $\newline$ $A = W \times H$
Given values: Given values for the area and width. $\newline$ Area $A = 33 \, \text{cm}^2$ $\newline$ Width $W = 7.5 \, \text{cm}$ (since $7 \frac{1}{2} \, \text{cm}$ is the same as $7.5 \, \text{cm}$ )
Rearrange formula: Rearrange the area formula to solve for height $H$ . $H = \frac{A}{W}$
Substitute values: Substitute the given values into the formula to find the height. $\newline$ $H = \frac{33 \, \text{cm}^2}{7.5 \, \text{cm}}$
Perform division: Perform the division to calculate the height. $H = 4.4\,\text{cm}$

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