If the diagonal of a square is decreased by 15%, then by what percent does the area of the square decrease?
Answer:
27.75%
- Let the length of the diagonal of the square be d. Length of the side of the square will then be รทรโร d / โ2, and the area of the square will be (d / โ2) ร (d / โ2) = 0.5d2
- After reducing the length of the diagonal by 15%, the new length of the diagonal will be:
= d -
d15 100
= 0.85d - Hence, the new area will be 0.5(0.85d)2 = 0.5 ร 0.7225d2.
- Decrease in the area = Old area - New area
= 0.5 d2 - 0.5 ร 0.7225d2
= 0.5 ร (1 - 0.7225) d2
= 0.5 ร 0.2775 d2 - Percentage decrease in the area =
ร 100 %Decrease in the area Old area
=
ร 100 %0.5 ร 0.2775 d2 0.5 d2
= 0.2775 ร 100 %
= 27.75% - Hence, when the diagonal of the square is decreased by 15%, then the area of the square decreases by 27.75%.