Question

Area of a rhombus is 24cm . If one
of its diagnol is6 cm then find the
measure of its other diagonal​

Answer 1

Given:-

• Area of a rhombus is 24 cm².
• One diagonal of its is 6 cm.

⠀

To find:-

• Measure of its other diagonal.

⠀

Solution:-

→ The rhombus may be fit into a rectangle as shown above (note that the measurements are not exact). One diagonal may represent the height of the rectangle and the measure of the other diagonal equals the horizontal sides of the rectangle. Each of the smaller rectangles were halved by a side of the rhombus (green). Therefore, the area of the rhombus is only half of the area of the rectangle that it fit in.

⠀

☆Area of rhombus = (D1 × D2)/2

⇛ 24 = 6 × D2/2

⇛ 24 × 2 = 6 × D2

⇛ 48 = 6 × D2

⇛ D2 = 48/6

⇛ D2 = 8 cm

⠀

Hence,

• the measure of other diagonal is 8 cm.

Answer 2

Correct Question-:

• Area of a rhombus is 24cm² . If oneof its diagonal is 6 cm Then , Find the measure of its other diagonal .

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{ Diagonal_{2}\: or \: D_{2} \: of \: Rhombus \: = \: 8cm }}}}}$

Explanation-:

Given,

• Length of Diagonal 1 or D¹ = 6 cm
• Area of Rhombus is 24 cm²

☆ Figure of Rhombus-:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(1,3){1.5}}\put(0,0){\line(1,0){5}}\put(5,0){\line(1,3){1.5}}\put(1.5,4.5){\line(1,0){5}}\qbezier(1.56,4.5)(1.56,4.5)(5,0)\qbezier(6.45,4.5)(6.45,4.5)(0,0)\put(-0.5,-0.5){\sf B}\put(1,4.8){\sf A}\put(5.2,-0.5){\sf C}\put(6.7,4.75){\sf D}\put(3,1.6){\sf O}\end{picture}$

To Find,

• Length of Diagonal or D² .

• $\underline{\boxed{\star{\sf{\purple{Area\:of \:Rhombus\::\frac {1}{2} \times Diagonal_{1} \times Diagonal_{2}}}}}}$

Here ,

• Diagonal 1 or D¹ of Rhombus = 6 cm
• Area of Rhombus = 24 cm ²
• Diagonal 2 or D² of Rhombus = ??

Now ,

• $\implies{\sf{\large {24 cm² = \frac {1}{2} \times 6 \times D_{2}}}}$
• $\implies{\sf{\large {24 cm² = 3 \times D_{2}}}}$
• $\implies{\sf{\large {\frac {3}{24} = D_{2}}}}$
• $\implies{\sf{\large {8cm = D_{2}}}}$

Hence,

• $\underline{\boxed{\star{\sf{\blue{ Diagonal_{2}\: or \: D_{2} \: of \: Rhombus \: = \: 8cm }}}}}$

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