The perimeter of a right triangle is 24 cm. Three times the length of the longer side minus two times the length of the shorter side exceeds hypotenuse by 2 cm.what are the lengths of all three sides??state method too.
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△ABC, let it be right angled at B. (Hypotenuse AC).
Let AB≤BC.
From 1st statement, AB+BC+CA=24
From 2nd statement, 3×BC−2×AB=AC+2
By Pythagoras' theorem AC2=AB2+BC2.
Now it's simply 3 equations and 3 variables, solving simultaneously gives
AC=10,BC=8,AB=6
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Can u please write the whole calculation so I can understand because up to here I also did easily
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Whenever you have n equations and n variables, just go on substituting from one to other and finally you reach 1 variable which leads to all others.
Our current Example is,
(i) a+b+c=24; (ii) 3a−2b=c+2; (iii) a2+b2=c2.
Use c=24−(a+b). So now you only have 2 equations and 2 variables.
(i) 3a−2b=24−(a+b)+2; (ii)a2+b2=(24−a−b)2
i.e. 4a−b=26 , 576+2ab−48a−48b=0 i.e. 24a+24b−ab=288
Now do substitution a=426+b
24(426+b)+24b−(426+b)b=288∴156+30b−4b2+26b=288
This is a quadratic in b, and has positive root 6.
Put b value in a=426+b=426+6=8
And finally, c=10
Sides 6,8,10.
As fast as possiblePlease help me
Please answer writing each step to the end..plse help me!!!
If someone understood the answer then please answer me writing it step by step upto the end in 12hrs plssssss.its urgent
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Done . Next time, give a reasonable heading to your note.
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Thanks very much...:-)