The lengths of parallel sides of a trapezium are (2x+3) and (x+8), and the distance between them is (x+4). If the area of the trapezium is 590, find the value of x.

Correct answer:

x =  -23.6667

Step-by-step explanation:

S=590 a = 2x+3 c = x+8 h = x+4 S = 2a+c h 590=((2x+3)+(x+8))/2 (x+4)  590=((2x+3)+(x+8))/2 (x+4) 1.5x211.5x+568=0 1.5x2+11.5x568=0  a=1.5;b=11.5;c=568 D=b24ac=11.5241.5(568)=3540.25 D>0  x1,2=2ab±D=311.5±3540.25 x1,2=3.833333±19.833333 x1=16 x2=23.666666667 x>0 x=x2=(23.6667)=371=233223.6667 a=2 x+3=2 (23.6667)+3=3133=443144.3333 c=x+8=(23.6667)+8=347=153215.6667 h=x+4=(23.6667)+4=359=193219.6667 S2=2a+c h=2(44.3333)+(15.6667) (19.6667)=590

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