Question

Help on my geometry please ! :(

Answer 1

Answer:  $y = 6\sqrt{2}$

=======================================================

Explanation:

The value of x = 6 since the two legs of a 45-45-90 triangle are always the same length. This triangle is isosceles.

The hypotenuse of any 45-45-90 triangle is exactly $\sqrt{2}$ times larger compared to the leg length.

This means,

$y = x\sqrt{2}\\\\y = 6\sqrt{2}$

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We can use the pythagorean theorem to confirm this

$a^2 + b^2 = c^2\\\\6^2 + x^2 = y^2\\\\6^2 + 6^2 = y^2\\\\72 = y^2\\\\y^2 = 72\\\\y = \sqrt{72}\\\\y = \sqrt{36*2}\\\\y = \sqrt{36}*\sqrt{2}\\\\y = 6\sqrt{2}$

Answer 2

Answer:

$y = 6 \sqrt{2}$

Step-by-step explanation:

if the measures both the acute angles of a right angled triangle are equal ( 45° ), then the two smaller sides are equal.

so, x = 6

now, by pythagorus theorem :

=》

$y {}^{2} = x {}^{2} + 6 {}^{2}$

=》

$y {}^{2} = 6 {}^{2} + 6 {}^{2}$

( because x = 6 )

=》

${y}^{2} = 2 \times 6 \times 6$

=》

$y = \sqrt{2 \times 6 \times 6}$

=》

$y = 6 \sqrt{2}$