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If D,E and F are the midpoints of the sides AB,AC and BC respectively of an equilateral triangle ABC, the ratio of the perimeters of triangle ABC to that of triangle DEF is?
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If D,E and F are the midpoints of the sides AB,AC and BC respectively ...
Solution:
Introduction:
In this question, we are given an equilateral triangle ABC with midpoints D, E and F of its sides AB, AC and BC respectively. We have to find the ratio of perimeters of triangle ABC to that of triangle DEF.
Explanation:
Let us first find out the lengths of sides of triangle ABC. As ABC is an equilateral triangle, all its sides are equal in length. Let us assume the length of each side to be 'a'. Therefore, we have:
AB = AC = BC = a
Now, let us find the lengths of sides of triangle DEF. We know that D, E and F are midpoints of the sides AB, AC and BC respectively. Therefore, we have:
DE = EF = FD = 1/2 * AB = 1/2 * AC = 1/2 * BC = 1/2 * a
Now, let us calculate the perimeters of triangles ABC and DEF. The perimeter of a triangle is the sum of lengths of its sides. Therefore, we have:
Perimeter of triangle ABC = AB + AC + BC = a + a + a = 3a
Perimeter of triangle DEF = DE + EF + FD = 1/2 * a + 1/2 * a + 1/2 * a = 3/2 * a
Therefore, the ratio of perimeters of triangles ABC and DEF is:
Perimeter of triangle ABC : Perimeter of triangle DEF = 3a : 3/2a = 2 : 1
Conclusion:
Hence, the ratio of perimeters of triangle ABC to that of triangle DEF is 2 : 1.
Introduction:
In this question, we are given an equilateral triangle ABC with midpoints D, E and F of its sides AB, AC and BC respectively. We have to find the ratio of perimeters of triangle ABC to that of triangle DEF.
Explanation:
Let us first find out the lengths of sides of triangle ABC. As ABC is an equilateral triangle, all its sides are equal in length. Let us assume the length of each side to be 'a'. Therefore, we have:
AB = AC = BC = a
Now, let us find the lengths of sides of triangle DEF. We know that D, E and F are midpoints of the sides AB, AC and BC respectively. Therefore, we have:
DE = EF = FD = 1/2 * AB = 1/2 * AC = 1/2 * BC = 1/2 * a
Now, let us calculate the perimeters of triangles ABC and DEF. The perimeter of a triangle is the sum of lengths of its sides. Therefore, we have:
Perimeter of triangle ABC = AB + AC + BC = a + a + a = 3a
Perimeter of triangle DEF = DE + EF + FD = 1/2 * a + 1/2 * a + 1/2 * a = 3/2 * a
Therefore, the ratio of perimeters of triangles ABC and DEF is:
Perimeter of triangle ABC : Perimeter of triangle DEF = 3a : 3/2a = 2 : 1
Conclusion:
Hence, the ratio of perimeters of triangle ABC to that of triangle DEF is 2 : 1.
Community Answer
If D,E and F are the midpoints of the sides AB,AC and BC respectively ...
Greetings
Hope you would like it
Since D, E, and F are the mid points of the sides AB, AC and BC
DE = 1/2 BC
EF = 1/2 AB
FD = 1/2 AC
Now,
Perimeter of ∆DEF/Perimeter of ∆ABC
=DE + EF + DF/ AB+ BC + AC
= 1/2 (AB + BC + AC)/ AB + BC + AC
= 1/2
Perimeter of ∆DEF: Perimeter of ∆ABC = 1:2
THANKING YOU
Hope you would like it
Since D, E, and F are the mid points of the sides AB, AC and BC
DE = 1/2 BC
EF = 1/2 AB
FD = 1/2 AC
Now,
Perimeter of ∆DEF/Perimeter of ∆ABC
=DE + EF + DF/ AB+ BC + AC
= 1/2 (AB + BC + AC)/ AB + BC + AC
= 1/2
Perimeter of ∆DEF: Perimeter of ∆ABC = 1:2
THANKING YOU
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If D,E and F are the midpoints of the sides AB,AC and BC respectively of an equilateral triangle ABC, the ratio of the perimeters of triangle ABC to that of triangle DEF is?
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If D,E and F are the midpoints of the sides AB,AC and BC respectively of an equilateral triangle ABC, the ratio of the perimeters of triangle ABC to that of triangle DEF is? 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 If D,E and F are the midpoints of the sides AB,AC and BC respectively of an equilateral triangle ABC, the ratio of the perimeters of triangle ABC to that of triangle DEF is? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If D,E and F are the midpoints of the sides AB,AC and BC respectively of an equilateral triangle ABC, the ratio of the perimeters of triangle ABC to that of triangle DEF is?.
If D,E and F are the midpoints of the sides AB,AC and BC respectively of an equilateral triangle ABC, the ratio of the perimeters of triangle ABC to that of triangle DEF is? 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 If D,E and F are the midpoints of the sides AB,AC and BC respectively of an equilateral triangle ABC, the ratio of the perimeters of triangle ABC to that of triangle DEF is? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If D,E and F are the midpoints of the sides AB,AC and BC respectively of an equilateral triangle ABC, the ratio of the perimeters of triangle ABC to that of triangle DEF is?.
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