Isosceles triangle

The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.

Correct result:

z =  2.8 dm

Solution:

r=5 dm 20 cm=2 dm  v=2+z r2=v2+(z/2)2  52=(2+z)2+(z/2)2  −1.25z2−4z+21=0 1.25z2+4z−21=0  a=1.25;b=4;c=−21 D=b2−4ac=42−4⋅1.25⋅(−21)=121 D>0  z1,2=−b±D2a=−4±1212.5 z1,2=−4±112.5 z1,2=−1.6±4.4 z1=2.8 z2=−6   Factored form of the equation:  1.25(z−2.8)(z+6)=0  z>0 z=z1=2.8=145=145 dm=2.8 dm v=2+z=2+2.8=245=4.8 dm r2=v2+(z/2)2=4.82+(2.8/2)2=5 dm

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