Question

Each side of a rhombus od 61 cm an one side of its diagonals is 22 cm long find the length of the other diagonal and the area of the rhombus

Answer 1

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Answer 2

Area of the rhombus is 1320 $cm^2$.

Step-by-step explanation:

Given:

As shown in the figure, let ABCD be the rhombus and O be the point on diagonals AC and BD.

Let’s take Δ ABO,

Let AC = 22 cm

AB = 61 cm is the hypotenuse

AO = 8 cm (half of AC as diagonals bisect)

Hence in the triangle ABO, using Pythagoras theorem,

$AO^2+BO^2=AB^2$

$11^2+BO^2=61^2$

$BO^2+121=3721$

$BO^2+121=3721-121$

$BO^2 = 3600$

$BO = \sqrt{3600}$

BO = 60

therefore diagonal BD = 2 BO

                                      =2 (60)

                                      = 120 cm

hence area of rhombus = $\frac{1}{2} \times AC \times BD$

                                        = $\frac{1}{2}\times 22 \times 120$

                                        = 1320 $cm^2$