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
∴ [tex]\frac{1}{2}[/tex] KM = 10 units
- Divide both sides by [tex]\frac{1}{2}[/tex]
∴ 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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