Question

The Quadrilateral ABCD has a area of 52 square inches and diagonal AC = 14.5 inches. Find the Length of diagonal BD is AC is perpendicular to AC

Answer 1

7.2 inches

Explanation:

Here is the complete question :

The Quadrilateral ABCD has a area of 52 square inches and diagonal AC = 14.5 inches. Find the Length of diagonal BD if AC is perpendicular to BD

the quadrilateral is a rhombus.

A rhombus is a four sides quadrilateral with the four sides equal in length

The area of a rhombus =
`(1)/(2) pq`

where p and q are the two diagonals

the above formula can be rewritten using the notation for diagonals provided in the question

52 in² =
`(1)/(2) AC BD`

52 =
`(1)/(2)` x 14.5 x BD

BD = (52 x 2) / 14.5

BD = 7.2 inches