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The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then find the length of its sides?
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The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then...
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The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then...
Solution:
Given, area of rhombus = 96 cm^2 and one diagonal = 16 cm.
We know that the area of a rhombus is given by the formula:
Area = (Product of diagonals)/2
So,
96 = (16 x d2)/2
where d2 is the other diagonal.
Simplifying the above equation, we get:
d2 = (2 x 96)/16
d2 = 12 cm
Now, we can use the Pythagorean theorem to find the length of the sides of the rhombus.
We know that the diagonals of a rhombus bisect each other at right angles. Therefore, we have two right triangles, each with one leg as half the length of a side of rhombus and hypotenuse as one of the diagonals.
Let a be the length of each side of the rhombus. Then,
(1/2 a)^2 + (1/2 d2)^2 = (16/2)^2
Simplifying the above equation, we get:
a^2 + 36 = 64
a^2 = 28
a = sqrt(28)
a = 2sqrt(7) cm
Therefore, the length of each side of the rhombus is 2sqrt(7) cm.
Given, area of rhombus = 96 cm^2 and one diagonal = 16 cm.
We know that the area of a rhombus is given by the formula:
Area = (Product of diagonals)/2
So,
96 = (16 x d2)/2
where d2 is the other diagonal.
Simplifying the above equation, we get:
d2 = (2 x 96)/16
d2 = 12 cm
Now, we can use the Pythagorean theorem to find the length of the sides of the rhombus.
We know that the diagonals of a rhombus bisect each other at right angles. Therefore, we have two right triangles, each with one leg as half the length of a side of rhombus and hypotenuse as one of the diagonals.
Let a be the length of each side of the rhombus. Then,
(1/2 a)^2 + (1/2 d2)^2 = (16/2)^2
Simplifying the above equation, we get:
a^2 + 36 = 64
a^2 = 28
a = sqrt(28)
a = 2sqrt(7) cm
Therefore, the length of each side of the rhombus is 2sqrt(7) cm.
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The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then find the length of its sides?
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The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then find the length of its sides? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then find the length of its sides? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then find the length of its sides?.
The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then find the length of its sides? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then find the length of its sides? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a rhombus is 96cm^2. lf one of its diagonal is 16 cm, then find the length of its sides?.
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