### If the diagonal of a square is decreased by 15%, then by what percent does the area of the square decrease?

**Answer:**

27.75%

**Step by Step Explanation:**

- Let the length of the diagonal of the square be
*d*. Length of the side of the square will then be ÷Â d / √2, and the area of the square will be (d / √2) × (d / √2) = 0.5d^{2} - 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 × 0.7225d^{2}. - Decrease in the area = Old area - New area

= 0.5 d^{2}- 0.5 × 0.7225d^{2}

= 0.5 × (1 - 0.7225) d^{2}

= 0.5 × 0.2775 d^{2} - Percentage decrease in the area =

× 100 %Decrease in the area Old area

=

× 100 %0.5 × 0.2775 d ^{2}0.5 d ^{2}

= 0.2775 × 100 %

= 27.75% - Hence, when the diagonal of the square is decreased by 15%, then the area of the square decreases by
**27.75%**.