Dimensions of the trapezoid

One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2

Correct result:

a =  12 cm
c =  11 cm
h =  10 cm

Solution:

a=h+h/5 c=1+h=1+10=1 S=115 cm2  S=a+c2 h 2S=((h+h/5)+(1+h))h  2 115=((h+h/5)+(1+h)) h 2.2h2h+230=0 2.2h2+h230=0  a=2.2;b=1;c=230 D=b24ac=1242.2(230)=2025 D>0  h1,2=b±D2a=1±20254.4 h1,2=0.22727273±10.2272727273 h1=10 h2=10.4545454545   Factored form of the equation:  2.2(h10)(h+10.4545454545)=0  h=h1=10  a=h+h/5=10+10/5=12 cm

Our quadratic equation calculator calculates it.

c=1+h=1+10=11 cm
h=10=10 cm   Verifying Solution:   S1=a+c2 h=12+112 10=115 cm2



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