Question

Construct a rhombus with side of length $5cm$ and an acute angle of ${45}^{\circ }$. The length of the longer diagonal of the rhombus is:

• A. $6.3cm$
• B. $3.8cm$
• C. $9.2cm$
• D. $10.6cm$

Answer 1

Answer: (C)

$9.2cm$

$\Rightarrow$ We know that all sides of rhombus are equal.

$\Rightarrow$ Draw a line segment AB = 5cm.

$\Rightarrow$ Construct an angle of ${45}^{\circ }$ at point A.

$\Rightarrow$ Cut off AD = 5cm.

$\Rightarrow$ Take D as center with radius 5cm, draw an arc.

$\Rightarrow$ Take B as a center with radius 5cm, draw an arc meeting at previous arc at point C.

$\Rightarrow$ Join AC, BD, BC and CD.

$\Rightarrow$ We have to measure length of larger diagonal i.e AC.

$\therefore$ $l\left(AC\right)=9.2cm$