Question

The area of a Rhombus is 119 sqm and its perimeter is 68m.Its altitude will be

1.) 7m

2.) 9m

3.) 11m

4.) 17m
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Answer 1

Required Answer -

7m

Given -

• Area of rhombus = 119m²

• Perimeter of rhombus = 68m

To find -

• It's altitude

Solution -

Since, rhombus has 4 equal sides, therefore it's perimeter is 4a, where a = side.

According to question -

→ 4 × side = 68m

→ Side = 68/4

→ Side = 17m

$\therefore$ Side of rhombus is 17m

Now,

It is given, area of rhombus i.e 119m².

Area of rhombus = Base × Altitude

119 = 17 × Altitude

Altitude = 119/17

Altitude = 7m

$\therefore$ The altitude of the rhombus is 7m

Verification -

i) Perimeter of rhombus = 4 × a

Perimeter of rhombus = 4 × 17

Perimeter of rhombus = 86m

ii) Area of rhombus = Base × Altitude

Area of rhombus = 17 × 7

Area of rhombus = 119m²

LHS = RHS

Hence, proved.

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Answer 2

Given:-

$\bigstar$The area of rhombus is 119 m

$\bigstar$The perimeter of rhombus is 68 m

To Prove:-

$\bigstar$The altitude of rhombus

Solution:-

$\bigstar$Let the side of rhombus be y inches

$\bigstar$Perimeter of rhombus = 68 m

$\longrightarrow\bold{4 \times side \: = \: 68 \: m} \\ \\ \longrightarrow\bold{4 \times y \: = \: 68 \: m} \\ \\ \longrightarrow\bold{y = \frac{68}{4} } \\ \\ \longrightarrow\bold{y \: = 17} \:$

$\bigstar$Hence, side of rhombus is 17 m.

$\bigstar$We know,

$\longrightarrow{ \boxed{ \boxed{ \bold{Side \: of \: r hombus \: = Base \: of \: rhombus</p><p> }}}} \:$

$\bigstar$Rhombus is a parallelogram with 4 equal sides. Hence, we can determine the area of rhombus as that of parallelogram.

$\bigstar$Let the height of rhombus be x inches

$\longrightarrow{ \boxed{ \boxed{ \bold{base \times height \: = 119 \: m \: }}}} \:$

$\longrightarrow \bold{17 \times x = 119} \\ \\ \longrightarrow\bold{x = \frac{119}{17} } \\ \\ \longrightarrow \bold{7 \: m}$

Hence, the altitude of the rhombus is 7 m