Answer:
9, 6√2, 2√3
Explanation:
In any question, use the pythagorean theorem:
In any right angle triangle,
a^2 + b^2 = c^2,
where c is the length of the hypotenuse (longest side, opposite to the 90º angle) and a,b, are the lengths of the other two sides.
In q1:
x^2 + 12^2 = 15^2
x^2 + 144 = 225
x^2 = 225-144
x^2 = 81
x = √81
x= 9
In q2:
6^2 + 6^2 = x^2
36 + 36 = x^2
72 = x^2
√72 = x
from here, you can split 72 into 36*2
√36 √2 = x
6√2 = x
In q3:
x^2 + √7 ^2 = √19^2
x^2 + 7 = 19
x^2 = 19 -7
x^2 = 12
x = √12
Split 12 into 4*3
x = √4√3
x = 2√3