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9514 1404 393

  14.14

Step-by-step explanation:

The diagonal of a square is √2 times the side length.

  AC = AB×√2

  AC = 10√2 ≈ 14.14

The diagonal of a square is the hypotenuse of an isosceles right triangle. If the sides of that are s and the diagonal is d, the Pythagorean theorem tells us ...

  d² = s² + s²

  d² = 2s²

  d = (√2)(√s²) = s√2

This relation holds for any isosceles right triangle, not just for the diagonal of this square. It is useful to remember.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

5+2x=a

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