If the side lengths a and B of the triangle ABC are two of the equations X & sup2; - 2 √ 3x + 2 = 0, and the area of the triangle ABC is √ 3 / 2, the third side C is obtained

If the side lengths a and B of the triangle ABC are two of the equations X & sup2; - 2 √ 3x + 2 = 0, and the area of the triangle ABC is √ 3 / 2, the third side C is obtained

Let a > b solve the equation, a = √ 3 + 1, B = √ 3-1
∵s=1/2absinC=√3/2
∠C=60°
Make the extension line of be vertical CA through B at e, CE = 1 / 2 (√ 3 + 1), EA = 1 / 2 (3 - √ 3)
BE=1/2(3+√3)
Using Pythagorean theorem to get C = √ 6
Draw your own picture and understand the knowledge of right triangle

The area formula of trapezoid is s = (a + b) H divided by 2. When a = B, why does trapezoid transform

When a = B, the top and bottom of the trapezoid are equal,
It becomes a parallelogram

Therefore, the trapezoidal area formula s = 1 / 2 (a + b) H requires h, which can be changed into behavior

h=2s/（a+b）
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It is known that the upper bottom a of trapezoid is 3, the height h is 5, and the area s is 20. According to the area formula s = 1 / 2 (a + b) h of trapezoid, the length of the lower bottom B is obtained

It is known that s = 1 / 2 (a + b) h, the upper bottom a = 3, the height h = 5, and the area s = 20. According to the trapezoid area formula s = 1 / 2 (a + b) h, the length of the lower bottom B is obtained
∵s=1/2（a+b）h,
∴b=2s÷h-a
=40÷5-3
=5