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The sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BEDC stands on the greatest side BC of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.?
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The sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BE...
We are given that a triangle with sides 39 cm ,42 cm and 45 cm.
A parallelogram stands on the greatest side =Base of parallelogram=45 cm
This question is part of UPSC exam. View all Class 9 courses
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The sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BE...
Given:
Sides of triangle ABC: 42cm, 39cm, and 45cm
To find:
Height of parallelogram BEDC
Approach:
1. First, we need to find the area of the triangle ABC using Heron's formula.
2. Then, we will find the base of the parallelogram, which is the same as the length of side BC.
3. Using the area of the triangle and the base of the parallelogram, we can find the height of the parallelogram.
Solution:
Step 1: Finding the area of triangle ABC using Heron's formula:
Heron's formula states that the area (A) of a triangle with sides a, b, and c is given by:
A = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, which is given by:
s = (a + b + c)/2
In this case, the sides of triangle ABC are 42cm, 39cm, and 45cm. So, we can calculate the semiperimeter as follows:
s = (42 + 39 + 45)/2
s = 126/2
s = 63
Now, we can calculate the area of the triangle using Heron's formula:
A = √(63(63-42)(63-39)(63-45))
A = √(63 * 21 * 24 * 18)
A = √(399168)
A ≈ 631.61 cm²
So, the area of triangle ABC is approximately 631.61 cm².
Step 2: Finding the base of the parallelogram:
The base of the parallelogram is the same as the length of side BC, which is 45cm.
Step 3: Finding the height of the parallelogram:
The area of a parallelogram is given by the formula:
Area = base * height
Since the area of the parallelogram BEDC is equal to the area of triangle ABC, we can equate the two areas:
631.61 cm² = 45 cm * height
Now, we can solve for the height of the parallelogram:
height = 631.61 cm² / 45 cm
height ≈ 14.03 cm
Therefore, the height of the parallelogram BEDC is approximately 14.03 cm.
Sides of triangle ABC: 42cm, 39cm, and 45cm
To find:
Height of parallelogram BEDC
Approach:
1. First, we need to find the area of the triangle ABC using Heron's formula.
2. Then, we will find the base of the parallelogram, which is the same as the length of side BC.
3. Using the area of the triangle and the base of the parallelogram, we can find the height of the parallelogram.
Solution:
Step 1: Finding the area of triangle ABC using Heron's formula:
Heron's formula states that the area (A) of a triangle with sides a, b, and c is given by:
A = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, which is given by:
s = (a + b + c)/2
In this case, the sides of triangle ABC are 42cm, 39cm, and 45cm. So, we can calculate the semiperimeter as follows:
s = (42 + 39 + 45)/2
s = 126/2
s = 63
Now, we can calculate the area of the triangle using Heron's formula:
A = √(63(63-42)(63-39)(63-45))
A = √(63 * 21 * 24 * 18)
A = √(399168)
A ≈ 631.61 cm²
So, the area of triangle ABC is approximately 631.61 cm².
Step 2: Finding the base of the parallelogram:
The base of the parallelogram is the same as the length of side BC, which is 45cm.
Step 3: Finding the height of the parallelogram:
The area of a parallelogram is given by the formula:
Area = base * height
Since the area of the parallelogram BEDC is equal to the area of triangle ABC, we can equate the two areas:
631.61 cm² = 45 cm * height
Now, we can solve for the height of the parallelogram:
height = 631.61 cm² / 45 cm
height ≈ 14.03 cm
Therefore, the height of the parallelogram BEDC is approximately 14.03 cm.
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The sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BEDC stands on the greatest side BC of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.?
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The sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BEDC stands on the greatest side BC of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.? 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 sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BEDC stands on the greatest side BC of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BEDC stands on the greatest side BC of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.?.
The sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BEDC stands on the greatest side BC of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.? 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 sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BEDC stands on the greatest side BC of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangle ABC are 42cm, 39cm and 45cm.A parallelogram BEDC stands on the greatest side BC of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.?.
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