Question

The lengths of the diagonals of a rhombus are 4x and 6x. What expressions give the perimeter and area of the rhombus? PLEASE HELP

Answer 1

Answer:

Area = 12x²

Perimeter = 4x√13

Step-by-step explanation:

Formula to be used for the area of a rhombus,

Area = $\frac{1}{2}(\text{Diagonal 1)}(\text{Diagonal 2})$

        = $\frac{1}{2}(4x)(6x)$

        = $12x^2$

Since, diagonals of a rhombus bisect each other at 90°.

OD = $\frac{1}{2}(BD)$

      = $\frac{1}{2}(4x)$

      = 2x

AO = $\frac{1}{2}(AC)$

      = $\frac{1}{2}(6x)$

      = 3x

By using Pythagoras theorem in ΔAOD,

AD² = AO² + DO²

AD² = (2x)² + (3x)²

AD² = 13x²

AD = x√13

Perimeter of a rhombus = 4(Side)

                                        = 4(x√13)

                                        = 4x√13