Trapezoid MO

The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other.

Calculate the perimeter and area of ​​the trapezoid.

Correct result:

p =  33.31
A =  69.25

Solution:

AC=12 CD=8  sinΘ=BCAC cosΘ=BCBD  cos2Θ+CDACcosΘ1=0 x2+CDACx1=0  x2+0.667x1=0  a=1;b=0.667;c=1 D=b24ac=0.667241(1)=4.4444444444 D>0  x1,2=b±D2a=0.67±4.442 x1,2=0.33333333±1.05409255339 x1=0.720759220056 x2=1.38742588672   Factored form of the equation:  (x0.720759220056)(x+1.38742588672)=0   Θ=435258"  BC=ACsinΘ=8.31822608044 AB=ACcosΘ=8.64911064067 AD=BC2+(ABCD)2=8.34351423258  o=AB+BC+CD+AD=33.31
A=(AB+CD)BC2=69.25



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