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ASAP!! ITS URGENT

Solve these problems. (Use a calculator with a square root function, and round off answers to two decimal places.)

ASAP!! ITS URGENT Solve these problems. (Use a calculator with a square root function-example-1
User Peterson
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Answer:

10. To find the area of rhombus ABCD, we can use the formula:

Area = (diagonal 1 x diagonal 2) / 2

We need to find the length of both diagonals. Since the diagonals of a rhombus are perpendicular and bisect each other, we can use the Pythagorean theorem to find the length of each diagonal.

AC is one diagonal, AB is a side of the rhombus, and BD is the other diagonal divided by 2 (since BD bisects AC):

BD = AC/2 = 10/2 = 5 cm

Using the Pythagorean theorem with AC and BD:

AC^2 = AB^2 + BD^2

AC^2 = 13^2 + 5^2

AC^2 = 169 + 25

AC^2 = 194

AC = sqrt(194) ≈ 13.93 cm

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

= (13.93 x 5) / 2

≈ 34.83 cm^2

Therefore, the area of rhombus ABCD is approximately 34.83 cm^2.

11. We know that the area of rhombus ABCD is 96 cm^2, and that BD is 8 cm. To find the length of AC, we can use the formula:

Area = (diagonal 1 x diagonal 2) / 2

Solving for diagonal 1 (AC):

AC = (2 x Area) / BD

= (2 x 96) / 8

= 24 cm

Therefore, the length of AC is 24 cm.

12. We know that AB is a side of the rhombus and that AB = 16 m. We also know that mZABD = 60 degrees. We can use trigonometry to find the length of the diagonals.

First, we can find the length of AD using the law of cosines:

AD^2 = AB^2 + BD^2 - 2(AB)(BD)cos(mZABD)

AD^2 = 16^2 + (2x)^2 - 2(16)(2x)cos(60)

AD^2 = 256 + 4 - 32x

AD^2 = 260 - 32x

AD = sqrt(260 - 32x)

Then, we can find the length of AC using the law of sines:

AC / sin(mZBAD) = AD / sin(mZABD)

AC / sin(120) = AD / sin(60)

AC = (AD x sin(120)) / sin(60)

AC = (sqrt(260 - 32x) x sqrt(3)) / 2

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

= [(sqrt(260 - 32x) x sqrt(3)) / 2] x 8 / 2

= 2(sqrt(260 - 32x) x sqrt(3))

≈ 67.29 m^2

Therefore, the area of rhombus ABCD is approximately 67.29 square meters.

13. We know that the perimeter of the rhombus is 20 mm, so each side is 5 mm. We also know that AC is one of the diagonals. To find the length of the other diagonal, we can use the Pythagorean theorem.

Let x be half the length of the other diagonal:

AC^2 = (2x)^2 + 5^2

x^2 = (AC^2 - 25) / 4

x = sqrt((AC^2 - 25) / 4)

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

= (AC x 2x) / 2

= xAC

= sqrt((AC^2 - 25) / 4) x AC

≈ 19.80 mm^2

Therefore, the area of rhombus ABCD is approximately 19.80 square millimeters.

User Shbfy
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