Question

Q-1
The area of rombus is 119cm² and it's perimeter is 56cm.
Find it's height.


Q-2
The area of rombus is 441cm² and it's height is 17.5cm. Find the length of each side of the rombus.

Q-3
The area of a rhombus is
equal to the area of triangle having base 24.8 cm and the corresponding height 16.5cm. If one of its diagonal of the rhombus is 22cm find the length of the other diagonal.

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Please answer the question fast

-@Aparna Priyadarshini




​

Answer 1

Step-by-step explanation:

1. area of rombus = 119cm²

perimeter = 56cm.

56 = 4 * side

side = 56/4 = 14cm

119cm²= 14*height

height = 119/14 = 8.5cm

2. area of rombus = 441cm²

height = 17.5cm.

441cm²= 17.5*side

side= 441/17.5 = 25.2cm

3.

the area of triangle = base * height

= 24.8*16.5 = 409.2cm²

area of triangle = area of rhombus = 409.2cm²

d1 of rhombus = 22cm

area of a rhombus = d1*d2

409.2cm²= 22cm *d2

d2= 409.2/22

d2 = 18.6cm

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Answer 2

$\star\;\;{\underline{\underline{\bf{\pink{Question\;1\;-}}}}}$

The area of rombus is 119cm² and it's perimeter is 56cm. Find it's height.

GivEn:-

• Area of rhombus = 119cm²

• Perimeter of rhombus = 56cm

To find:-

• Height of rhombus

SoluTion:-

As we know that,

☯ Perimeter of rhombus = 4 × length of its side

$\therefore$ All side of rhombus are euqal!

$:\implies$ Length of its side = $\sf \dfrac{Perimeter}{4}$

$:\implies$ Length of its side = $\sf \cancel{ \dfrac{54}{4}}$

$:\implies$ Length of its side = 14cm

☯ Area of rhombus = base(side) × Altitude

$:\implies$ Altitude = $\sf \dfrac{Area}{Base}$

$:\implies$ Altitude = $\sf \cancel{ \dfrac{119}{14}}$

$:\implies$ Altitude = 8.5 cm

$\dag$ Hence, Altitude of rhombus is 8.5 cm.

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$\star\;\;{\underline{\underline{\bf{\pink{Question\;2\;-}}}}}$

The area of rombus is 441cm² and it's height is 17.5cm. Find the length of each side of the Rhombus.

GivEn:-

• Area of rhombus = 441cm²

• Height of rhombus = 17.5 cm

To find:-

• length of each side of the Rhombus.

SoluTion:-

As we know that,

☯ Area of rhombus = Side × Altitude

$:\implies$ Side = $\sf \dfrac{Area}{Altitude}$

$:\implies$ Side = $\sf \dfrac{441}{17.5}$

$:\implies$ Side = 25.2 cm

$\dag$ Hence, Side of rhombus is 25.2 cm.

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$\star\;\;{\underline{\underline{\bf{\pink{Question\;3\;-}}}}}$

The area of a rhombus is equal to the area of triangle having base 24.8 cm and the corresponding height 16.5cm. If one of its diagonal of the rhombus is 22cm find the length of the other diagonal.

GivEn:-

• Area of rhombus = Area of triangle

• Base of rhombus = 24.8 cm

• Height of rhombus = 16.5 cm

• One of the diagonal of rhombus = 22cm

To find:-

• Length of other diagonal.

SoluTion:-

Let other diagonal of rhombus be x cm.

GivEn that,

☯ Area of rhombus = Area of triangle

$:\implies\sf \dfrac{1}{2} \times base \times height = \dfrac{Product\;of\;diagonals}{2} \quad\bigg\lgroup\bf By\; Deriving\;the\;formula \bigg\rgroup$

$:\implies\sf \dfrac{1}{2} \times 24.8 \times 16.5 = \dfrac{22 \times x}{2}$

$:\implies\sf 204.6 \times 2 = 22 \times x$

$:\implies\sf \dfrac{204.6 \times 2}{22} = x$

$:\implies\sf \dfrac{409.2}{22} = x$

$:\implies$ x = 18.6 cm

$\dag$ Hence, Length of diagonal is 18.6 cm.

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