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The perimeter of right triangle is 300m . its sides are in ratio 3:5:7. find area of the triangle . Also find height corresponding to the longest side.?
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The perimeter of right triangle is 300m . its sides are in ratio 3:5:7...
Problem Statement:
Find the area of a right triangle whose perimeter is 300m and sides are in the ratio of 3:5:7. Also, find the height corresponding to the longest side.
Solution:
Let the sides of the triangle be 3x, 5x and 7x. Since it is a right triangle, we can apply Pythagoras theorem.
According to Pythagoras theorem,
Hypotenuse^2 = Base^2 + Height^2
So, for the given triangle,
(7x)^2 = (3x)^2 + (5x)^2
49x^2 = 9x^2 + 25x^2
49x^2 = 34x^2
x^2 = 0
x = 0 (not possible)
Therefore, the sides of the triangle cannot be in the ratio of 3:5:7. This means that the question is incorrect or some information is missing.
However, if we assume that the ratio of the sides is 6:10:14 instead of 3:5:7, then we can proceed with the solution as follows:
Let the sides of the triangle be 6x, 10x and 14x.
Perimeter of the triangle = 300m
6x + 10x + 14x = 300
30x = 300
x = 10
Therefore, the sides of the triangle are 60m, 100m and 140m
Area of the triangle:
Area of a right triangle = 1/2 * Base * Height
Since the longest side is the hypotenuse, we can take it as the base.
Base = 140m
Now, we need to find the height corresponding to the longest side.
Let the height be h.
We know that,
Area of the triangle = 1/2 * Base * Height
Area of the triangle = 1/2 * 140 * h
Area of the triangle = 70h
Also, we know that,
Perimeter of the triangle = 300m
6x + 10x + 14x = 300
30x = 300
x = 10
Therefore,
Height + Base + Hypotenuse = 300
h + 60 + 140 = 300
h = 100
Final Answer:
Therefore, the sides of the triangle are 60m, 100m and 140m. The area of the triangle is 7000 sq.m and the height corresponding to the longest side is 100m.
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The perimeter of right triangle is 300m . its sides are in ratio 3:5:7. find area of the triangle . Also find height corresponding to the longest side.?
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The perimeter of right triangle is 300m . its sides are in ratio 3:5:7. find area of the triangle . Also find height corresponding to the longest side.? 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 perimeter of right triangle is 300m . its sides are in ratio 3:5:7. find area of the triangle . Also find height corresponding to the longest side.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of right triangle is 300m . its sides are in ratio 3:5:7. find area of the triangle . Also find height corresponding to the longest side.?.
The perimeter of right triangle is 300m . its sides are in ratio 3:5:7. find area of the triangle . Also find height corresponding to the longest side.? 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 perimeter of right triangle is 300m . its sides are in ratio 3:5:7. find area of the triangle . Also find height corresponding to the longest side.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of right triangle is 300m . its sides are in ratio 3:5:7. find area of the triangle . Also find height corresponding to the longest side.?.
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