The hypotenuse of a right triangle is 26 cm and the difference between the other two sides is 14cm.find the two sides
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Let the two sides be x and y.
a/c to the ques,
x-y=14....(1)
and by Pythagoras theorem, x²+y²=z²
So.
x²+y²=676...(2)
Squaring both sides in 1
We get
x²+y² -2xy=196
From 2,
676-196=2xy
480=2xy
240=xy...(3)
By the identity,
(x+y)²= x²+y² +2xy
By 2 and 3 we have,
(x+y)²= 676+480
(x+y)²=1156
(x+y)=34 (we cant take -34 as the length is not negative.).....(4)
From 1 and 4 We have,
2x=48
x=24 and y=10.
So the other two sides are 24cm and 10cm.
Hope this helps.
a/c to the ques,
x-y=14....(1)
and by Pythagoras theorem, x²+y²=z²
So.
x²+y²=676...(2)
Squaring both sides in 1
We get
x²+y² -2xy=196
From 2,
676-196=2xy
480=2xy
240=xy...(3)
By the identity,
(x+y)²= x²+y² +2xy
By 2 and 3 we have,
(x+y)²= 676+480
(x+y)²=1156
(x+y)=34 (we cant take -34 as the length is not negative.).....(4)
From 1 and 4 We have,
2x=48
x=24 and y=10.
So the other two sides are 24cm and 10cm.
Hope this helps.
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