Question

1. solve x and y for the diagram.

x = 6; y = \sqrt{12}
x = 36; y = 12\sqrt{10}
x = 36; y = 3\sqrt{90}
x = 6; y = 4\sqrt{10}

Explanation:

Step1: Use geometric mean for x

$\frac{4}{12} = \frac{12}{x} \implies 4x = 144$

Step2: Calculate x

$x = \frac{144}{4} = 36$

Step3: Use Pythagoras for y

$y = \sqrt{12^2 + 36^2} = \sqrt{144 + 1296}$

Step4: Simplify y

$y = \sqrt{1440} = 12\sqrt{10}$

Answer:

x = 36; y = 12√10