Question

The area of□ABCD is 100 in? and AC-2-BD. Find the diagonals. x 2x AC= 2x

How do I find x?

Answer 1

Answer 2

SOLUTION :

AC = 2 BD and Area ABCD = 100 in^2

Let diagonal BD = 2x

So, diagonal AC = 4x 

Diagonals are perpendicular to each other. 

So, Area of ABCD

= 2 * Area of triangle ABC

= 2 * (1/2 * base * height)

= base * height (of triangle ABC)

= 4x * x

= 4x^2

So,

4x^2 = 100 in^2 (given area of ABCD)

=> x = sqrt(100/4) = 5 in.

So,

AC = 4x = 4*5 = 20 in. (ANSWER)

BD = 2x = 2*5 = 10 in (ANSWER)