Question

The perimeter of a rhombus is 260cm and height is 10cm. If one diagonal is 0.25m, find the lenght of other diagonal in metres

Answer 1

Answer:

Length of other diagonal is 0.52 cm.

Step-by-step explanation:

Here,

Perimeter of rhombus = 260 cm

From the properties of quadrilaterals :

• Perimeter of rhombus = 4 x side
• Area of rhombus = 1 / 2 x product of diagonals = a side x perpendicular on that side

= > Perimeter of rhombus = 4 side

= > 260 cm = 4 side

= > 65 cm = side( magnitude of side of rhombus )

Therefore,

= > Area of rhombus = 65 cm x 10 cm

= > Area of rhombus = 650 cm^2

Also,

= > Area of rhombus = 1 / 2 x product of diagonals

= > 650 cm^2 = 1 / 2 x ( 0.25 x 100 cm ) x other diagonal

= > 650 cm^2 = 1 / 2 x 25 cm x other diagonal

= > ( 650 x 2 ) / 25 cm = other diagonal

= > 52 cm = other diagonal

= > 52 / 100 m = 0.52 m = length of other diagonal.

Hence, length of other diagonal is 0.52 cm.

Answer 2

$\huge{\underline{\underline{\mathbb{\pink{Solution}}}}}$

${\underline{\mathbb{\blue{Given}}}}$

Perimeter of rhombus = 260 cm

Diagonal of rhombus ( d1l ) = 0.25 m

Height of rhombus = 10 cm = 0.1 m

Let 2nd diagonal of rhombus as x .

Perimeter of rhombus = 4a

$\mathbb \pink{a \: = side \: of \: rhombus}$

Calculation →

～> 4a = 260

～> a. = 260/4

～> a. = 65 cm

～> 65cm = 0.65 m

$\mathbb \blue{area \: of \: rhombus \: = base \times height}$

Calculation →

～> Area = 0.1 × 0.65

～> Area =0.065 m

$\mathbb \pink{area \: of \: rhombus \: is \: also \: = \frac{1}{2} \times (d1 \times d2}$

$\frac{1}{2} (0.25)(x) = 0.065$

0.125 x = 0.065

$x = \frac{0.065}{0.125}$

x = 0.52

x is 2nd diagonal hence d2 = 0.52 m