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Marina CMI [18]
3 years ago
11

The perimeter of a rectangle is 70cm. if its length is decreased by 5cm and its width is increased by 5cm, its area will increas

e by 50 cm^2. Find the length and the width of the original rectangle.
Mathematics
1 answer:
Valentin [98]3 years ago
3 0

Answer:

l=25, w=10

Step-by-step explanation:

2(25)+2(10)=70

25*10=250

25-5=20

10+5=15

20*15=300

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The missing measures are listed below:

  1. m \angle 1 = m \angle 3 = m \angle 6 = 59^{\circ}
  2. m\angle 2 = m\angle 4 = m\angle 5 = m \angle 11 = 31^{\circ}
  3. m\angle 7 = m\angle 8 = m\angle 9 = m\angle 10 = 118^{\circ}

<h3>Procedure - Finding missing angles in a quadrilateral</h3>

In this question we must determine the measures of the <em>missing</em> angles by both <em>geometric</em> and <em>algebraic</em> means, whose procedure is presented below:

  1. x = 59^{\circ} Given
  2. m \angle 3 = 59^{\circ} Alternate internal angles
  3. m \angle 11 = 31^{\circ} Complementary angles
  4. m \angle 4 = 31^{\circ} Alternate internal angles
  5. m \angle 6 = 59^{\circ} Isosceles triangle
  6. m \angle 9 = 62^{\circ} Sum of internal angles in a triangle
  7. m \angle 10 = 118^{\circ} Supplementary angles
  8. m \angle 8 = 62^{\circ}, m\angle 7 = 118^{\circ} Vertical angles
  9. m \angle 2 = 31^{\circ} Sum of internal angles in a triangle
  10. m \angle 5 = 31^{\circ} Sum of internal angles in a triangle
  11. m \angle 1 = 59^{\circ} Sum of internal angles in a triangle/Result

The missing measures are listed below:

  1. m \angle 1 = m \angle 3 = m \angle 6 = 59^{\circ}
  2. m\angle 2 = m\angle 4 = m\angle 5 = m \angle 11 = 31^{\circ}
  3. m\angle 7 = m\angle 8 = m\angle 9 = m\angle 10 = 118^{\circ}

To learn more on angles, we kindly invite to check this verified question: brainly.com/question/15767203

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