Find the value of x. The drawing is not to scale.
2 answers:
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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
