R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.

Correct result:

S =  158.9 dm2

Solution:

c2=a2+b2 a=c−6 a=b+3 a>0 b>0  b2−2⋅6⋅b−2⋅6⋅3−62=0  b=6+2⋅62+2⋅6⋅3=16.39 dm a=b+3=19.39 dm  S=12ab=12(b+3)b=158.9 dm2c^2=a^2+b^2 \ \\ a = c-6 \ \\ a = b + 3 \ \\ a>0 \ \\ b>0 \ \\ \ \\ b^2-2 \cdot 6 \cdot b - 2 \cdot 6 \cdot 3-6^2=0 \ \\ \ \\ b = 6 + \sqrt{ 2\cdot 6^2+2\cdot 6\cdot 3} = 16.39 \ dm \ \\ a = b+ 3 = 19.39 \ dm \ \\ \ \\ S = \dfrac{1}{2}ab = \dfrac{1}{2}(b+3)b = 158.9 \ \text{dm}^2

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