Perpendicular leg

Calculate the area of a right triangle whose longer perpendicular is six dm shorter than the hypotenuse and three dm longer than the shorter perpendicular.

Correct answer:

S =  158.9423 dm2

Step-by-step explanation:

a = c−6 a = 3+b a2+b2 = c2  (c−6)2+(a−3)2 = c2 (c−6)2+((c−6)−3)2=c2  c2−30c+117=0  p=1;q=−30;r=117 D=q2−4pr=302−4⋅1⋅117=432 D>0  c1,2​=2p−q±D​​=230±432​​=230±123​​ c1,2​=15±10.392305 c1​=25.392304845 c2​=4.607695155  c=c1​=25.3923≐25.3923 dm a=c−6=25.3923−6≐19.3923 dm b=a−3=19.3923−3≐16.3923 dm  S=2a⋅ b​=219.3923⋅ 16.3923​≐158.9423 dm2   Verifying Solution:  c3​=a2+b2​=19.39232+16.39232​≐25.3923 dm

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