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Bess [88]
3 years ago
14

A challenge to all math experts...

Mathematics
1 answer:
earnstyle [38]3 years ago
7 0

Answer:

75

Step-by-step explanation:

<em><u>Refer to attachment</u></em>

As the first step extending the segment BC until intersection with AD.

Since ∠A + ∠B = 90° we get right triangle by extending CB

Naming the segments a, b, c, d as pictured

<u>The are of (ABCD) is equal to sum of areas of two right triangles:</u>

  • Area = 1/2c(a+b) + 1/2bd

<u>Substitute d with a-c as a = c+d, then:</u>

  • Area = 1/2(ac+bc) + 1/2b(a-c) = 1/2(ac + bc + ab - bc) = 1/2(ab + ac)
  • Area = 1/2(ab+ac)

<u>Applying Pythagorean to small triangle:</u>

  • 10² = b² + (a-c)²
  • 100 = b² + a² - 2ac + c²

<u>Applying Pythagorean to bigger triangle:</u>

  • 20² = (a+b)² + c²
  • 400 = a² + 2ab + b² + c²

<u>Subtracting equations we got:</u>

  • 400 - 100 = a² + 2ab + b² + c² - (b² + a² - 2ac + c²)
  • 300 = 2ab + 2ac

<u>This gives us the 4 times of the area which is 1/2(ab + ac), so the area is </u>

  • 300/4 = 75

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