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Morgan is designing a rectangular quilt. The quilt will be
1(3)/(5)m wide and will have an area of
6m^(2).
How long is the quilt?
m

Morgan is designing a rectangular quilt. The quilt will be $1 \frac{3}{5} \mathrm{~m}$ wide and will have an area of $6 \mathrm{~m}^{2}$ . $\newline$ How long is the quilt? $\newline$ m

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Scale drawings: word problems

Full solution

Q. Morgan is designing a rectangular quilt. The quilt will be

1 \frac{3}{5} \mathrm{~m}

wide and will have an area of

6 \mathrm{~m}^{2}

.

\newline

How long is the quilt?

\newline

m

Convert to Improper Fraction: Convert the mixed number for the width of the quilt to an improper fraction. $\newline$ $1\frac{3}{5}$ can be converted to an improper fraction by multiplying the whole number by the denominator of the fraction, adding the numerator, and placing the result over the original denominator. $\newline$ $1\frac{3}{5} = (1 \times 5 + 3)/5 = (5 + 3)/5 = \frac{8}{5}$ $\newline$ The width of the quilt is $\frac{8}{5}$ meters.
Use Area Formula: Use the area formula for a rectangle to find the length. $\newline$ The area $A$ of a rectangle is given by the formula $A = \text{width} \times \text{length}$ . $\newline$ We know the area is $6$ square meters $(6\,\text{m}^2)$ and the width is $\frac{8}{5}$ meters. $\newline$ Let's denote the length of the quilt as ' $L$ '. $\newline$ So, the equation is $6 = \left(\frac{8}{5}\right) \times L$ .
Solve for Length: Solve for the length $L$ . To find $L$ , divide both sides of the equation by $\frac{8}{5}$ . $L = \frac{6}{(\frac{8}{5})}$ To divide by a fraction, multiply by its reciprocal. $L = 6 \times (\frac{5}{8})$ $L = \frac{30}{8}$ $L = 3.75$ The length of the quilt is $3.75$ meters.

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