Isosceles triangle

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

Correct answer:

z =  2.8 dm

Step-by-step explanation:

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​=2a−b±D​​=2.5−4±121​​ z1,2​=2.5−4±11​ z1,2​=−1.6±4.4 z1​=2.8 z2​=−6  z>0 z=z1​=2.8=514​ v=2+z=2+2.8=524​=4.8 dm r2​=v2+(z/2)2​=4.82+(2.8/2)2​=5 dm

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