R triangle

Calculate the right triangle area whose longer leg is 7 dm shorter than the hypotenuse and 10 dm longer than the shorter leg.

Final Answer:

S =  363.627 dm2

Step-by-step explanation:

c2=a2+b2 a = c−7 a = b + 10 a>0 b>0  (a+7)2=a2+(a−10)2  −a2+34a−51=0 a2−34a+51=0  p=1;q=−34;r=51 D=q2−4pr=342−4⋅1⋅51=952 D>0  a1,2​=2p−q±D​​=234±952​​=234±2238​​ a1,2​=17±15.427249 a1​=32.427248621 a2​=1.572751379  a=a1​=32.4272≐32.4272 dm b=a−10=32.4272−10≐22.4272 dm  S=21​⋅ a⋅ b=21​⋅ 32.4272⋅ 22.4272≐363.627 dm2   Verifying Solution:  c=a2+b2​=32.42722+22.42722​≐39.4272 dm

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algebraarithmeticplanimetricsUnits of physical quantitiesGrade of the word problem

 
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