Question

Rectangle J K L M is shown. Diagonals are drawn from point J to point L and from point K to point M and intersect in the middle. All angles are right angles. The length of J M is 12 and the distance from M to the center point is 10.
What is the perimeter of rectangle JKLM?

32 units
44 units
56 units
64 units

Answer 1

The perimeter of the rectangle JKLM is 56 units ⇒ 3rd answer

Step-by-step explanation:

Let us revise the properties of a rectangle:

• Each two opposite sides are parallel and equal
• The for angles are equal (4 right angles)
• The two diagonals are equal and bisect each other
• The center of the rectangle is the point of intersection of the two diagonals

In rectangle JKLM

∵ JL and KM are the two diagonals

∴ JL = KM

∵ The distance from M to the center point is 10 units

- The center point is the mid-point of each diagonal

∴ $\frac{1}{2}$ KM = 10 units

- Divide both sides by $\frac{1}{2}$

∴ KM = 20 units

∴ JL = 20 units

In Δ JML

∵ m∠JML = 90 ⇒ an angle of the rectangle

∵ JM = 12 units ⇒ given

∵ JL = 20 units ⇒ proved

- By using the Pythagoras theorem (hypotenuse)² = (leg 1)² + (leg 2)²

∵ JM and ML are the legs and JL is the hypotenuse

∴ (20)² = (12)² + (ML)²

∴ 400 = 144 + (ML)²

- Subtract 144 from both sides

∴ 256 = (ML)²

- Take √ for both sides

∴ 16 = ML

∴ The length of ML is 16 units

The formula of the perimeter of a rectangle is P = 2(length + width)

∵ ML is its length

∵ JM is its width

∴ P = 2(16 + 12) = 56 units

The perimeter of the rectangle JKLM is 56 units

Learn more:

You can learn more about the rectangles in brainly.com/question/6564657

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Answer 2

Answer:

The answer is C on Edge 2020

Step-by-step explanation:

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