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

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Area and perimeter: word problems

Full solution

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

33

and a width of

7 \frac{1}{2}

. What is the height of this painting?

Understand the problem: Understand the problem. $\newline$ We are given the area of a rectangle and its width. We need to find the height. The formula for the area of a rectangle is $\text{Area} = \text{Width} \times \text{Height}$ .
Convert to improper fraction: Convert the width to an improper fraction for easier calculation. $\newline$ The width is given as $7\frac{1}{2}$ , which is a mixed number. To convert it to an improper fraction, we multiply the whole number by the denominator and add the numerator, then place that result over the original denominator. $\newline$ $7\frac{1}{2} = (7 \times 2 + 1) / 2 = (14 + 1) / 2 = 15/2$
Use area formula: Use the area formula to solve for the height. $\newline$ Area = Width $\times$ Height $\newline$ $33 = (15/2) \times$ Height $\newline$ To find the height, we divide the area by the width. $\newline$ Height = Area $\div$ Width $\newline$ Height = $33 \div (15/2)$
Perform division: Perform the division to solve for the height. $\newline$ To divide by a fraction, we multiply by its reciprocal. $\newline$ Height $= 33 \times \left(\frac{2}{15}\right)$ $\newline$ Height $= \frac{66}{15}$
Simplify fraction: Simplify the fraction to find the height. $\newline$ $\frac{66}{15}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . $\newline$ Height = $\left(\frac{66 \div 3}{15 \div 3}\right)$ $\newline$ Height = $\frac{22}{5}$ $\newline$ Height = $4 \frac{2}{5}$

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