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The perimeter of a square is 48. What is the length of its diagonal?

$12\sqrt{2}$

$\sqrt{12}$

$24\sqrt{2}$

$48\sqrt{2}$

$2\sqrt{12}$

Explanation

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

The perimeter of a square is 48. What is the length of its diagonal?

$12\sqrt{2}$

$\sqrt{12}$

$24\sqrt{2}$

$48\sqrt{2}$

$2\sqrt{12}$

Explanation

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

How much more area does a square with a side of 2r have than a circle with a radius r? Approximate π by using 22/7.

12/14 square units

1/7 square units

4/7 square units

6/7 square units

Explanation

The area of a circle is given by A = πr2 or 22/7r2

The area of a square is given by A = s2 or (2r)2 = 4r2

Then subtract the area of the circle from the area of the square and get 6/7 square units.

The area of a square is $25 cm^{2}$ . If the square is enlarged by a factor of 2, what is the perimeter of the new square?

$40\ cm$

$50\ cm$

$75\ cm$

$80\ cm$

$100\ cm$

Explanation

The area of a square is given by $A = s^{2}$ so we know the side is 5 cm. Enlarging by a factor of two makes the new side 10 cm. The perimeter is given by , so the perimeter of the new square is 40 cm.

How much more area does a square with a side of 2r have than a circle with a radius r? Approximate π by using 22/7.

12/14 square units

1/7 square units

4/7 square units

6/7 square units

Explanation

The area of a circle is given by A = πr2 or 22/7r2

The area of a square is given by A = s2 or (2r)2 = 4r2

Then subtract the area of the circle from the area of the square and get 6/7 square units.

The area of a square is $25 cm^{2}$ . If the square is enlarged by a factor of 2, what is the perimeter of the new square?

$40\ cm$

$50\ cm$

$75\ cm$

$80\ cm$

$100\ cm$

Explanation

If a completely fenced-in square-shaped yard requires 140 feet of fence, what is the area, in square feet, of the lot?

140

1225

4900

Explanation

Since the yard is square in shape, we can divide the perimeter(140ft) by 4, giving us 35ft for each side. We then square 35 to give us the area, 1225 feet.

If a completely fenced-in square-shaped yard requires 140 feet of fence, what is the area, in square feet, of the lot?

140

1225

4900

Explanation

Since the yard is square in shape, we can divide the perimeter(140ft) by 4, giving us 35ft for each side. We then square 35 to give us the area, 1225 feet.

Square X has 3 times the area of Square Y. If the perimeter of Square Y is 24 ft, what is the area of Square X, in sq ft?

112

144

108

Explanation

Find the area of Square Y, then calculate the area of Square X.

If the perimeter of Square Y is 24, then each side is 24/4, or 6.

A = 6 * 6 = 36 sq ft, for Square Y

If Square X has 3 times the area, then 3 * 36 = 108 sq ft.

Square_with_diagonal

Find the area of a square with a diagonal of .

$3.125cm^{2}$

Not enough information to solve

$6.25cm^{2}$

$\dpi{100} 4.25cm^{2}$

$5.0cm^{2}$

Explanation

A few facts need to be known to solve this problem. Observe that the diagonal of the square cuts it into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: $1:\sqrt{2}$ .