A designer enlarged both the length and the width of a rectangular carpet by 60 percent. The new carpet was too large so the designer was asked to reduce its length and its width by 25 percent. By what percent was the area of the final item greater than the area of the original?

300%

Step-by-step explanation:

Let the length of the carpet be L.

Let the width of the carpet be W.

The original area of the carpet is:

A = L * W = LW

The length and width are enlarged by 60%.

The new length is:

L + (L * 60/100) = L + 0.6L = 1.6L

The new width is:

W + (W * 60/100) = W + 0.6W = 1.6W

The length and width are then reduced by 25%.

The new length is:

1.6L + (1.6L * 25/100) = 1.6L + 0.4L = 2L

The new width is:

1.6W + (1.6W * 25/100) = 1.6W + 0.4W = 2W

The new area will be:

A = 2L * 2W = 4LW

To find the percentage increase in the area, we subtract the original area from the new area and divide by the original area:

4LW - LW = 3LW

% increase is:

= 300%

The area of the final item is 300% greater than the original item.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.