Question

The area of rhombus is 120 cm2

and one of the diagonals is 8 cm. Find the other

diagonal.​

Answer 1

Given:–

• Area of rhombus is 120 cm²
• One diagonal of rhombus is 8 cm

To Find:–

• What is the length of the other diagonal of rhombus ?

Solution:–

Let the length of other diagonal of rhombus be 'x' cm

We know that the formula for finding the area of rhombus is:-

$\large{\boxed{\bf{\star \: Area = \dfrac{1}{2} \times d_1 \times d_2 \: \star}}}$

On putting the values in the formula, we get:

$\sf{\implies 120 = \dfrac{1}{\cancel{2}} \times \cancel{8} \times x}$

$\sf{\implies 120 = 4 \times x}$

$\sf{\implies \cancel\dfrac{120}{4} = x}$

$\large{\underbrace{\bf{ \star \: 30 = x \: \star}}}$

Hence, the length of the other diagonal is 30 cm

______________________

$\Large\underline\mathbf{More \: To \: Know!}$

➸ Opposite sides are equal.

➸ Opposite angles are equal.

➸ Diagonals bisect each other.

➸ Diagonals are equal.

➸ Diagonals bisect vertex angles.

➸ Diagonals are perpendicular.

______________________

Answer 2

$\underline{\underline{\textsf{\maltese\:\: Given :}}}$

☞ Area of rhombus = 120cm²

☞ Length of one diagonal = 8cm

$\underline{\underline{\textsf{\maltese\:\: To Find :}}}$

☞ Length of other diagonal = ?

$\underline{\underline{\textsf{\maltese\:\: Diagram :}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(1,3){1.5}}\put(0,0){\line(1,0){5}}\put(5,0){\line(1,3){1.5}}\put(1.5,4.5){\line(1,0){5}}\put(-0.5,-0.5){\sf D}\put(1,4.8){\sf A}\put(5.2,-0.5){\sf C}\put(6.7,4.75){\sf B} \qbezier(1.5,4.5)(1.5,4.5)(5.01,-.01) \put(2.7,1.9){\bf8 cm} \put(3,3){\bf {Area =120 \bf{cm}^2 }} \end{picture}$

$\underline{\underline{\textsf{\maltese\:\: Solution :}}}$

Area of rhombus = $\frac{1}{2}$ × Product of its diagonals

⇒ Area of rhombus = $\frac{1}{2}$ × d₁ × d₂

⇒ 120cm² = $\frac{1}{2}$ × AC × DB

⇒ 120cm² = $\frac{1}{2}$ × 8cm × DB

⇒ 120cm² × 2 × $\frac{1}{8}$ = DB

⇒ 30cm = DB

⇒ DB = 30cm

∴ Length of other diagonal is 30cm.