If one angle of a rhombus is 60° and the length of a side is 8 cm, find the lengths of its diagonals.

Each side of rhombus ABCD is 8 cm. So, AB = BC = CD = DA = 8 cm. Let ∠A = 60°. In ∆ABD, AB = AD ∠ADB = ∠ABD = x (let) (Angles opposite to equal sides are equal.) ⇒ ∠ADB + ∠ABD + ∠DAB = 180° ⇒ x + x + 60° = 180° ⇒ 2x + 60° = 180° ⇒ 2x = 180° - 60° ⇒ 2x = 120° ⇒ x = ⇒ x = 60°. Since, all angles = 60°. Hence, △ABD is an equilateral triangle. So, BD = 8 cm. As we know, the diagonals of a rhombus bisect each other at right angles AO = OC, BO = OD = 4cm and ∠AOB = 90° Now, in right ∆AOB By Pythagoras theorem, ⇒ AB 2 = AO 2 + OB 2 ⇒ 8 2 = AO 2 + 4 2 ⇒ 64 = AO 2 + 16 ⇒ AO 2 = 64 – 16 = 48 ⇒ AO = cm. But, AC = 2AO ⇒ AC = cm. Hence, length of diagonals = 8 cm and cm.

Using ruler and compasses only, construct a parallelogram ABCD with AB = 5 cm, AD = 2.5 cm and ∠BAD = 45°. If the bisector of ∠BAD meets DC at E, prove that ∠AEB is a right angle.

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In the adjoining figure, ABCD is a rhombus and DCFE is a square. If ∠ABC = 56°, find
(i) ∠DAG
(ii) ∠FEG
(iii) ∠GAC
(iv) ∠AGC.

Mathematics

If one angle of a rhombus is 60° and the length of a side is 8 cm, find the lengths of its diagonals.

Rectilinear Figures

Related Questions

Using ruler and compasses only, construct a parallelogram ABCD with AB = 5 cm, AD = 2.5 cm and ∠BAD = 45°. If the bisector of ∠BAD meets DC at E, prove that ∠AEB is a right angle.

In the adjoining figure, ABCD is a rhombus and DCFE is a square. If ∠ABC = 56°, find
(i) ∠DAG
(ii) ∠FEG
(iii) ∠GAC
(iv) ∠AGC.

Find the size of each lettered angle in the following figure:

Find the size of each lettered angle in the following figure:

Mathematics

If one angle of a rhombus is 60° and the length of a side is 8 cm, find the lengths of its diagonals.

Rectilinear Figures

Related Questions

Using ruler and compasses only, construct a parallelogram ABCD with AB = 5 cm, AD = 2.5 cm and ∠BAD = 45°. If the bisector of ∠BAD meets DC at E, prove that ∠AEB is a right angle.

In the adjoining figure, ABCD is a rhombus and DCFE is a square. If ∠ABC = 56°, find(i) ∠DAG(ii) ∠FEG(iii) ∠GAC(iv) ∠AGC.

Find the size of each lettered angle in the following figure:

Find the size of each lettered angle in the following figure:

In the adjoining figure, ABCD is a rhombus and DCFE is a square. If ∠ABC = 56°, find
(i) ∠DAG
(ii) ∠FEG
(iii) ∠GAC
(iv) ∠AGC.