In a right angled triangle, the sides forming the right angle differ by 7 cm. Find its sides, if its perimeter is 40cm.
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Answered by
10
Let the length of the base = x
Then,
hypotenuse = 33-2x
perpendicular = x+7
So, by pythagoras theorem,
1089+4x²-132x=x²+x²+49+14x
2x²+1040-146x=0
x²+520-73x=0
x²-73x+520=0
x²-8x-65x+520=0
x(x-8)-65(x-8)=0
(x-8)(x-65)=0
x-8=0 or x-65=0
therefore, x=8 or x=65
x={8,65}
If x=8
the sides are 8,15,17 cm.
If x=65
the sides are 65,72,-137 cm.
Since, the answer for second value is in negative we will negotiate it.
Therefore, x=8 and the sides are 8 cm , 15 cm & 17 cm.
Then,
hypotenuse = 33-2x
perpendicular = x+7
So, by pythagoras theorem,
1089+4x²-132x=x²+x²+49+14x
2x²+1040-146x=0
x²+520-73x=0
x²-73x+520=0
x²-8x-65x+520=0
x(x-8)-65(x-8)=0
(x-8)(x-65)=0
x-8=0 or x-65=0
therefore, x=8 or x=65
x={8,65}
If x=8
the sides are 8,15,17 cm.
If x=65
the sides are 65,72,-137 cm.
Since, the answer for second value is in negative we will negotiate it.
Therefore, x=8 and the sides are 8 cm , 15 cm & 17 cm.
Answered by
3
Answer:
8,15,17
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