Answer:
option B
Step-by-step explanation:
since two two angles are 45 degree it can be said that the other two smaller legs of a triangle are equal.
Hypotenuse is 90 degree because it is opposite of 90 degree (which is a largest angle).
out of these four options A and B are the possible answers.because its two sides are equal. Now we should check which one is correct by using pythagoras theorem.
for option A
a^2 + b^2 = c^2
[tex](\frac{\sqrt{3} }{2} )^2[/tex] +[tex](\frac{\sqrt{3} }{2})^2[/tex] = [tex]\sqrt{\sqrt{2} }[/tex]
[tex]\frac{3}{4} + \frac{3}{4} = 2[/tex]
take lcm of denominator
[tex]\frac{3+3}{4} =2[/tex]
[tex]\frac{6}{4}=2[/tex]
[tex]\frac{3}{2 } =2[/tex]
this can not be the sides of the right angle because according to the pythagoras theorem to be the right angle sum of square of two smaller sides of a triangle must equal to the square of hypotenuse .But here it is not equal.so it cannot be the sides of right angle triangle.
For option B
a^2 + b^2 = c^2
[tex](3\sqrt{2} )^2 + (3\sqrt{2})^2 = 6^2[/tex]
[tex]3*3*2 + 3*3*2 =36[/tex]
[tex]18 + 18 =36[/tex]
[tex]36 = 36[/tex]
since both sides are equal it satisfies the pythagoras theorem.
therefore answer is option B.
