I have no idea how to draw these please help

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Answer:

  1, 2: draw x as the altitude of a right triangle

  3: draw x as double the altitude of the right triangle

Step-by-step explanation:

Consider the right-triangle geometry in the attachment. All of the right triangles are similar, so the ratios of corresponding sides are equal.

  short side / long side = x/r = s/x

You may notice this compares to the required relation in problem 1.

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If you multiply this out, you get ...

  x² = rs   ⇒   x = √(rs)

This compares to the required relation in problem 2.

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So, you append the two line segments to each other so they make segment AB, find their midpoint D (using a perpendicular bisector construction), then draw the (semi-)circle centered at that midpoint. The perpendicular at X will intersect the circle at C, a distance of x from the line rs. (A perpendicular to a line at a point construction is required to create XC.)

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For problem 3, you simply need to double the length √(rs) that you found in the previous constructions. A simple way to do this is to draw a circle, not a semicircle. Then point C' on the lower half of the circle will be 2√(rs) from point C.

_____

In the attached, we have shown right triangle ABC for discussion purposes above. Segments AC and BC are not needed for your purpose.

Point of clarification: AX = r, BX = s, CX = x.

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1 point
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12 -3 + 15 - 2 x 8 = p
3 x 12 + 2 x 15 + 8 = p
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