Question

abcd is a rhombus with one diagonal equal to 18cm. and length of each side equal to 15cm. find the length of the other diagonal and area of rhombus

Answer 1

ABCD is a rhombus,in which AB=BC=CD=DA=15cm. Diagonals AC and BD cut at point O. Diagonal BD=18cm , BO=18/2=9cm.

In right angled triangle BOC:-

OC^2=BC^2-OB^2

OC^2=(15)^2-(9)^2=144

OC=12cm

AC=2×OC=2×12cm=24cm.

area=1/2*base*height
=1/2*15*24cm²
=180cm²

Answer 2

the length of other diagonal =24 cm

area of rhombus =216 cm².

Given:

Length of one diagonal = 18

Length of each side = 15

To find:

Length of other diagonal and area of rhombus

Solution:

In a rhombus there are four right angled triangles, in which diagonals form the base and height and side of the rhombus is hypotenuse

So, in the rhombus ABCD, O being the center of diagonal

AB = 15

AC = 18

So, OA = 1/2 * 18 = 9 [Diagonals of rhombus bisect each other]

In Δ OAB

OA² + OB² = AB²

9² + OB² = 15²

OB² = 15² - 9²

OB² = 225 - 81

OB² = 144

OB = $\sqrt{144}$

OB = 12

BD = 2* 12 = 24cm [ BD is other diagonal]

Area of rhombus = 1/2 * product of diagonals

= 1/2 * 18*24

= 9*24

= 216 cm²

Hence, the length of other diagonal is 24 cm and area of rhombus is 216 cm².

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