Respuesta :

The correct answer is:

8 in.

Explanation:

The quadrilaterals with perpendicular diagonals are a square and a rhombus.  In both of these, the diagonals are perpendicular bisectors of one another.

Since a square is a rhombus, we will use the formula for the area of a rhombus to solve this problem:

A = (diagonal 1 × diagonal 2)/2

Let diagonal 1 = AC and diagonal 2 = BD.  We know that AC = 14.5 and the area, A, is 58:
58 = (14.5 × BD)/2

Multiply both sides by 2:
58×2 = ((14.5×BD)/2)×2
116 = 14.5×BD

Divide both sides by 14.5:
116/14.5 = 14.5×BD/14.5
8 = BD

The measure of the second diagonal, BD, is 8 inches.
adioabiola

The length of the diagonal BD if AC ⊥ BD is; BD= 8in

Quadrilaterals

The two kinds of quadrilaterals with perpendicular diagonals are

  • a square and
  • a rhombus.

In both of these, the diagonals are perpendicular(90°) bisectors of one another.

Using the formula for evaluating the Area, A of a rhombus; we have;

  • A = (D(1) × D(2))/2

Where;

D1 = AC and D2 = BD.

Given that AC = 14.5 and the area, A, is 58: we have;

  • 58 = (14.5 × BD)/2

By Cross-product; we have;

  • 58×2 = 14.5×BD

  • 116 = 14.5×BD

Dividing both sides by 14.5:

  • 116/14.5 = 14.5×BD/14.5

BD = 8in.

Read more on quadrilaterals;

https://brainly.com/question/8823615

Otras preguntas