If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, find the other diagonal.

Let ABCD be the rhombus and the diagonals intersect at point O. Let diagonal AC = 16 cm. We know that, Diagonals of rhombus bisect each other at right angles. ∴ AO = OC = = 8 cm and BO = OD = x cm (let). In right angle triangle AOB, By pythagoras theorem, ⇒ (Hypotenuse) 2 = (Perpendicular) 2 + Base 2 ⇒ AB 2 = AO 2 + OB 2 ⇒ 10 2 = 8 2 + x 2 ⇒ 100 = 64 + x 2 ⇒ x 2 = 100 - 64 ⇒ x 2 = 36 ⇒ x = = 6 cm. From figure, ⇒ BD = BO + OD = 6 + 6 = 12 cm. Hence, length of other diagonal = 12 cm.

In the given figure, ∠B = 90°, XY // BC, AB = 12 cm, AY = 8 cm and AX : XB = 1 : 2 = AY : YC. Find the lengths of AC and BC.

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In △ ABC, ∠B = 90°. Find the sides of the triangle, if :
(i) AB = (x - 3) cm, BC = (x + 4) cm and AC = (x + 6) cm
(ii) AB = x cm, BC = (4x + 4) cm and AC = (4x + 5) cm.

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In the given figure, diagonals AC and BD intersect at right angle. Show that :
AB² + CD² = AD² + BC²

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Mathematics

If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, find the other diagonal.

Pythagoras Theorem

Related Questions

In the given figure, ∠B = 90°, XY // BC, AB = 12 cm, AY = 8 cm and AX : XB = 1 : 2 = AY : YC. Find the lengths of AC and BC.

In △ ABC, ∠B = 90°. Find the sides of the triangle, if :
(i) AB = (x - 3) cm, BC = (x + 4) cm and AC = (x + 6) cm
(ii) AB = x cm, BC = (4x + 4) cm and AC = (4x + 5) cm.

In the given figure, diagonals AC and BD intersect at right angle. Show that :
AB² + CD² = AD² + BC²

Mathematics

If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, find the other diagonal.

Pythagoras Theorem

Related Questions

In the given figure, ∠B = 90°, XY // BC, AB = 12 cm, AY = 8 cm and AX : XB = 1 : 2 = AY : YC. Find the lengths of AC and BC.

In △ ABC, ∠B = 90°. Find the sides of the triangle, if :(i) AB = (x - 3) cm, BC = (x + 4) cm and AC = (x + 6) cm(ii) AB = x cm, BC = (4x + 4) cm and AC = (4x + 5) cm.

In the given figure, diagonals AC and BD intersect at right angle. Show that :AB2 + CD2 = AD2 + BC2

In △ ABC, ∠B = 90°. Find the sides of the triangle, if :
(i) AB = (x - 3) cm, BC = (x + 4) cm and AC = (x + 6) cm
(ii) AB = x cm, BC = (4x + 4) cm and AC = (4x + 5) cm.

In the given figure, diagonals AC and BD intersect at right angle. Show that :
AB² + CD² = AD² + BC²