Explanation:
10)
again, drawing the height into a right triangle creates 3 right triangles : the original one, and the 2 on both sides of the height.
all these 3 triangles are similar to each other (the angles must be the same).
therefore the ratio of 2 sides in one triangle must be the same as the ratio of the corresponding 2 sides in the other triangles.
so,
x/36 = 64/x
x² = 64×36
x = sqrt(64×36) = 8×6 = 48
11)
same principle.
x/36 = 100/x
x² = 100×36
x = sqrt(100×36) = 10×6 = 60
12)
same as 11)
x/9 = (16+9)/x = 25/x
x² = 25×9
x = sqrt(25×9) = 5×3 = 15