Question

1. The lengths of the diagonals of a rhombus are 18 cm and 24 cm. Then, the length of the side of the rhombus is [1] (1) 20 cm (2) 10 cm (3) 5 cm (4) 15 cm

Answer 1

GIVEN :-

• Length of diagonals of rhombus are 18 cm and 24 cm.

TO FIND :-

• The length of the side of rhombus.

TO FIND :-

➠ As we know that,

$\to \boxed{ \red{ \bf \:Area \: (rhombus) = \dfrac{1}{2} \times d_{1} \times d_{2}}}$

$\to \rm \: \dfrac{1}{ \cancel{2}} \times \cancel{18}\: cm \: \times 24 \: cm \\ \\ \to \rm \: 9 \times 24 \: cm ^{2} \\ \\ \to \red{ \rm \: 216 \: cm ^{2} }$

➠ Hence the area of rhombus is 216 cm². Now let's calculate the the side of the Rhombus,

$\to \boxed{ \red{ \bf \: Area(rhombus) = \{side \} ^{2} }} \\ \\ \to \rm \: 216 = \{side \} ^{2} \\ \\ \to \rm \: side = \sqrt{216} \\ \\ \to \red{ \rm \: side = 14.69 \approx \: 15 \: cm}$

➠ Hence the side of rhombus is 15 cm.

Hence option (4) is correct ✔

ADDITIONAL INFORMATION :-

➠ Rhombus :- A Quadrilateral having four equal sides is called rhombus.

➠ It is popularly known as equilateral quadrilateral. Due to having all the equal sides.

➠ Opposite angles of rhombus are equal.

➠ Sum of interior angle of rhombus is 360°.

➠ The diagonals diagonals of rhombus intersect each other at 90°.

Answer 2

Solution :

$\underline{\bf{Given\::}}}$

The length of the diagonals of a rhombus are 18 cm & 24 cm. Attachment of a  diagram of rhombus according to the question;

$\underline{\bf{Explanation\::}}}$

As we know that diagonals of rhombus divide into four congruent right triangles (90°)°.

A/q

• BD = 24 cm
• AC = 18 cm

Diagonals = OB = OD & OA = OC

$\mapsto\sf{OB = \dfrac{1}{2} BD}\\\\\mapsto\sf{OB = \dfrac{1}{\cancel{2}} \times \cancel{24}}\\\\\mapsto\bf{OB = 12\:cm}$

&

$\mapsto\sf{OA = \dfrac{1}{2} AC}\\\\\mapsto\sf{OA = \dfrac{1}{\cancel{2}} \times \cancel{18}}\\\\\mapsto\bf{OA = 9\:cm}$

$\underline{\boldsymbol{By\:using\:Pythagoras\:theorem\::}}}$

$\longrightarrow\sf{(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2} }\\\\\longrightarrow\sf{(AB)^{2} = (OA)^{2} + (OB)^{2} }\\\\\longrightarrow\sf{(AB)^{2} = (9)^{2} + (12)^{2} }\\\\\longrightarrow\sf{(AB)^{2} = 81 + 144}\\\\\longrightarrow\sf{(AB)^{2} = 225}\\\\\longrightarrow\sf{AB=\sqrt{225} }\\\\\longrightarrow\bf{AB= 15\:cm}$

Thus;

The length of the side of rhombus will be 15 cm .

Option (4)