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The width of a rectangle is two-thirds its length if the perimeter is 210 m find the dimension of the rectangle?
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The width of a rectangle is two-thirds its length if the perimeter is ...
Understanding the Problem
To find the dimensions of a rectangle where the width is two-thirds of its length and the perimeter is 210 m, we can set up a mathematical representation.
Defining Variables
- Let the length of the rectangle be L meters.
- Then the width, W, can be expressed as:
W = (2/3) * L
Perimeter Formula
The perimeter (P) of a rectangle is given by the formula:
P = 2 * (L + W)
Since the perimeter is 210 m, we can substitute the values:
210 = 2 * (L + W)
Substituting Width in the Perimeter Equation
- Substitute W with (2/3) * L:
210 = 2 * (L + (2/3) * L)
- Simplify the equation:
210 = 2 * (L + (2/3)L)
210 = 2 * (5/3)L
210 = (10/3)L
Solving for Length
- Multiply both sides by 3 to eliminate the fraction:
630 = 10L
- Now, divide by 10:
L = 63 m
Finding Width
- Now, substitute L back to find W:
W = (2/3) * 63
W = 42 m
Final Dimensions
- Length (L): 63 m
- Width (W): 42 m
In conclusion, the dimensions of the rectangle are:
- Length: 63 meters
- Width: 42 meters
To find the dimensions of a rectangle where the width is two-thirds of its length and the perimeter is 210 m, we can set up a mathematical representation.
Defining Variables
- Let the length of the rectangle be L meters.
- Then the width, W, can be expressed as:
W = (2/3) * L
Perimeter Formula
The perimeter (P) of a rectangle is given by the formula:
P = 2 * (L + W)
Since the perimeter is 210 m, we can substitute the values:
210 = 2 * (L + W)
Substituting Width in the Perimeter Equation
- Substitute W with (2/3) * L:
210 = 2 * (L + (2/3) * L)
- Simplify the equation:
210 = 2 * (L + (2/3)L)
210 = 2 * (5/3)L
210 = (10/3)L
Solving for Length
- Multiply both sides by 3 to eliminate the fraction:
630 = 10L
- Now, divide by 10:
L = 63 m
Finding Width
- Now, substitute L back to find W:
W = (2/3) * 63
W = 42 m
Final Dimensions
- Length (L): 63 m
- Width (W): 42 m
In conclusion, the dimensions of the rectangle are:
- Length: 63 meters
- Width: 42 meters
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The width of a rectangle is two-thirds its length if the perimeter is 210 m find the dimension of the rectangle?
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The width of a rectangle is two-thirds its length if the perimeter is 210 m find the dimension of the rectangle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The width of a rectangle is two-thirds its length if the perimeter is 210 m find the dimension of the rectangle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The width of a rectangle is two-thirds its length if the perimeter is 210 m find the dimension of the rectangle?.
The width of a rectangle is two-thirds its length if the perimeter is 210 m find the dimension of the rectangle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The width of a rectangle is two-thirds its length if the perimeter is 210 m find the dimension of the rectangle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The width of a rectangle is two-thirds its length if the perimeter is 210 m find the dimension of the rectangle?.
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