(a) The value of the variable x, is x = 3√2.
(b) The value of variable y is y = √14
How to calculate the value of the variables?
(a) The value of the variables is calculated by applying Pythagoras theorem as follows;
x² = y² - 3² ----- (1)
considering the bigger triangle;
y² = (6 + 3)² - h² ------ (2)
h² = 6² + x² ------------- (3)
Substitute (3) into (2);
y² = (6 + 3)² - (6² + x²)
y² = 9² - 6² - x²
y² = 45 - x² ----- (4)
substitute the value of y² in (1) into (4);
y² = 45 - x²
x² + 3² = 45 - x²
2x² = 45 - 9
2x² = 36
x² = 36 / 2
x² = 18
x = √18
x = 3√2
(b) The value of y is calculated as follows;
h² = y² - 2² ----- (1)
y² = (2 + 5)² - z²
y² = 7² - z² ----- (2)
h² = z² - 5² ----- (3)
substitute (2) into (3);
h² = z² - 5²
h² = 7² - y² - 5²
h² = 24 - y² ------ (4)
substitute (1) into (4);
y² - 2² = 24 - y²
2y² = 24 + 4
2y² = 28
y² = 14
y = √14