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Dr. Sanskari ?⚕️?⚕️ 6 years, 2 months ago
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Yogita Ingle 6 years, 2 months ago
Let us assume √2 is rational number.
a rational number can be written into he form of p/q
√2=p/q
p=√2q
Squaring on both sides
p²=2q²__________(1)
.·.2 divides p² then 2 also divides p
.·.p is an even number
Let p=2a (definition of even number,'a' is positive integer)
Put p=2a in eq (1)
p²=2q²
(2a)²=2q²
4a²=2q²
q²=2a²
.·.2 divides q² then 2 also divides q
Both p and q have 2 as common factor.
But this contradicts the fact that p and q are co primes or integers.
Our supposition is false
.·.√2 is an irrational number.
Posted by Shivam Sangwan 6 years, 2 months ago
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Yogita Ingle 6 years, 2 months ago
Perimeter of that triangle = 60cm
the measure of hypotaneous = 25cm
then the rest sides must measure = 60-25
= 35
let one side be x
then, thw measure of the third side must be 35 - x
using pythagoras theorem
(25)^2 =(x)22 + (35-x)2
625 = x2 + x2 - 70x + 1225
x2 + x2 - 70x + 1225 = 625
x2 + x2 - 70x + 1225 -625 = 0
2 x2 - 70x + 600 = 0
2x2 - 40x - 30 x + 600= 0
2x (x-20) -30 ( x - 20) = 0
(x-20)(2x-30)=0
x -20 = 0
x = 20
2x -30 =0
2x =30
x = 15
so,
one of the side measure either 20 cm 15 cm
if one side measure 20cm then the other must measure 35 -20 = 15cm
and if it measured 15 cm then the other side measure 35-15 = 20 cm
so,we will get 20cm and 15 cm as our remaining sides.
one of then will be height and the other misy be the base,
now apply the formula of area of triangle i.e
(1/2) (height)(base)
= (1/2 )(20)(15)
= 150 cm2
so, the area of that triangle will be 150 cm2.
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