Question

if the diagonal of a square is decreased by 35%, then by what percent does the area of the square decrease? brainliest for correct answer pls quick the correct answer is 51% but i need working asap

Answer 1

Step-by-step explanation:

Let the side of the square be a.

Length of diagonal = √a² + a²

= a√2

When length of diagonal is decreased 35% then length of current diagonal is ,

d' = (1 - 35/100) x a√2

= 65/100 x a√2

= 0.65 x a√2

Let the side of the new square be a' .

d' = a'√2

0.65 x a√2 = a'√2

a' = 0.65a

Now area of new square = (0.65a)²

= 0.4225a²

Percent decrease in area is = a² - 0.4225a²/a² x 100

=57%