Rectangles

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The sum of the lengths of three sides of a rectangle is 572 inches; the width of the rectangle is 60% of its length. Give its area in square inches.

It is impossible to determine the area from the given information.

$40,560 \textrm{ in}^{2}$

$29,040 \textrm{ in}^{2}$

$48,400\textrm{ in}^{2}$

$67,600\textrm{ in}^{2}$

Explanation

Since the width of the rectangle is 60% of its length, we can write .

However, it is not clear from the problem which three sides - two lengths and a width or two widths and a length - we are choosing to have sum 572 inches. Depending on the three sides chosen, we can either set up

$2.6L \div 2.6 = 572 \div 2.6$

$2.2L \div 2.2 = 260$

Since the length cannot be determined with certainty, neither can the width, and, subsequently, neither can the area.

A rectangle is two feet shorter than twice its width; its perimeter is six yards. Give its area in square inches.

$2,816 \textrm{ in}^{2}$

$7,128 \textrm{ in}^{2}$

$1,386 \textrm{ in}^{2}$

$2,475 \textrm{ in}^{2}$

$2,772 \textrm{ in}^{2}$

Explanation

The length of the rectangle is two feet, or 24 inches, shorter than twice the width, so, if is the width in inches, the length in inches is

Six yards, the perimeter of the rectangle, is equal to $36 \times 6 = 216$ inches. The perimeter, in terms of length and width, is , so we can set up the equation:

$6W \div 6 = 264 \div 6$

The length and width are 64 inches and 44 inches; the area is their product, which is

$44 \times 64 = 2,816$ square inches

Rectangle

Give the area of the above rectangle in square feet.

$216 \textrm{ ft}^{2}$

$532\textrm{ ft}^{2}$

$576 \textrm{ ft}^{2}$

$33 \textrm{ ft}^{2}$

$66 \textrm{ ft}^{2}$

Explanation

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

$8 \textrm{ yd} \times 3 \textrm{ ft/yd} = 24 \textrm{ ft}$

$3 \textrm{ yd} \times 3 \textrm{ ft/yd} = 9 \textrm{ ft}$

Use the area formula, substituting :

$A = 24 \times 9 = 216$ square feet

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

Explanation

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

To find the area of a rectangle, we must perform the following:

$A_{Rectangle}=l*w$

Where l and w are our length and width.

This means we need to multiply the given measurements. Be sure to use the right units!

And we have our answer. It must be centimeters squared, because we are dealing with area.

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is $4 \times 1 = 4$ , and its area is $1^{2} = 1$ .

The perimeter of the first square is $\frac{7}{4} \times 4 = 7$ , and its sidelength is $7 \div 4 = \frac{7}{4}$ . The area of this square is therefore $\left (\frac{7}{4} \right )^{2} =\frac{49}{16}$ .

The ratio of the areas is therefore $\frac{49}{16} : 1 = 49:16$ .

Annie has a piece of wallpaper that is by . How much of a wall can be covered by this piece of wallpaper?

Explanation

This problem asks us to calculate the amount of space that the wallpaper will cover. The amount of space that something covers can be described as its area. In this case area is calculated by using the formula $A=l \times w$