If perimeter of a rectangle is 14/8/15 m and its length is 4/2/3m find its breadth
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I read that as 14 8/15 m and 4 2/3 m , 14/8/15 makes little sense.
P = 2L + 2W
14 8/15 = 2(4 2/3) + 2W
218/15 - 28/3 = 2W
2W = 26/5
W = 13/5 m or 2.6 m
btw, metric units of measurement usually aren't stated as
fractions like that, it would defeat the beauty and purpose
of the metric system.
To find the breadth of the rectangle, we can use the formula for the perimeter of a rectangle.
Perimeter = 2 * (length + breadth)
Given that the perimeter is 14/8/15 m and the length is 4/2/3 m, we can substitute these values into the formula and solve for the breadth.
14/8/15 = 2 * (4/2/3 + breadth)
Start by simplifying the expression inside the parentheses:
14/8/15 = 2 * (6/3 + breadth)
Next, add the fractions and simplify:
14/8/15 = 2 * (2 + breadth)
14/8/15 = 4 + 2*breadth
Subtract 4 from both sides:
14/8/15 - 4 = 2*breadth
Multiply both sides by 1/2:
(14/8/15 - 4) * 1/2 = breadth
Simplify the left side:
(14/8/15) * 1/2 - 4/2 = breadth
Multiply the numerators and denominators:
(14 * 1) / (8 * 2 * 15) - 4/2 = breadth
Simplify:
14/240 - 2 = breadth
Convert both fractions to have a common denominator of 240:
14/240 - (2 * 120)/240 = breadth
Combine the fractions:
(14 - 240)/240 = breadth
Simplify:
-226/240 = breadth
Now, we can reduce the fraction:
-113/120 = breadth
Therefore, the breadth of the rectangle is -113/120 m.
To find the breadth of the rectangle, we need to use the given information about the perimeter and length of the rectangle.
Let's start by understanding the formula for the perimeter of a rectangle:
Perimeter = 2 × (Length + Breadth)
Here, the perimeter is given as 14/8/15 m and the length is given as 4/2/3 m.
Now, let's substitute these values into the formula and solve for the breadth:
14/8/15 = 2 × (4/2/3 + Breadth)
To simplify the equation, we need to convert the fractions into a common denominator:
14/8/15 = 2 × (12/6/9 + Breadth)
Next, we can simplify the equation further by multiplying both sides by the common denominator (24):
(24 × 14/8/15) = 2 × (24 × 12/6/9 + 24 × Breadth)
336/8/15 = 2 × (288/6/9 + 24 × Breadth)
336/8/15 = 2 × (48/3/9 + 24 × Breadth)
Now, let's simplify the equation:
336/8/15 = 2 × (16/1/9 + 24 × Breadth)
336/8/15 = 2 × (144/9 + 24 × Breadth)
336/8/15 = 2 × (16 + 24 × Breadth)
Finally, let's solve for the breadth by isolating the variable:
336/8/15 = 32 + 48 × Breadth
336/8/15 - 32 = 48 × Breadth
336/8/15 - 32 = 48 × Breadth
48 × Breadth = 336/8/15 - 32
48 × Breadth = (336 - 32 × (8/15)) / (8/15)
48 × Breadth = (336 × 15/8 - 32 × 8/15) / (8/15)
48 × Breadth = (5040/8 - 256/15) / (8/15)
48 × Breadth = (630 - 17.067) / 1.066
48 × Breadth = 612.933 / 1.066
Breadth = 612.933 / (48 × 1.066)
Now, divide the numerator by the denominator:
Breadth ≈ 12.76 meters
Therefore, the breadth of the rectangle is approximately 12.76 meters.