The breadth of a rectangular field is 75% of its length.If the diagonal of the field is 100 m,what is the area of the field ?
B=.75L
100=sqrt(B^2+L^2)
100=L sqrt(.75^2+1)
100=L sqsrt(9/16+16/16)=L sqrt(25/16)
100=L*5/4
L=80
B=3/4 * 80=60
area=BL
To find the area of the rectangular field, we first need to determine its length and breadth.
Let's assume the length of the field is "L" meters.
According to the given information, the breadth of the rectangular field is 75% of its length, which means the breadth is (75/100) * L = 0.75L meters.
To find the length and breadth, we can use the Pythagorean theorem with the diagonal being the hypotenuse:
Diagonal = √(Length^2 + Breadth^2)
Substituting the given values:
100 = √(L^2 + (0.75L)^2)
Simplifying the equation:
100 = √(L^2 + 0.5625L^2)
100 = √(1.5625L^2)
Squaring both sides:
100^2 = 1.5625L^2
10000 = 1.5625L^2
Dividing both sides by 1.5625:
L^2 = 10000 / 1.5625
L^2 = 6400
Taking the square root of both sides:
L = √6400
L = 80
The length of the field is 80 meters.
Now, we can calculate the breadth:
Breadth = 0.75 * L
Breadth = 0.75 * 80
Breadth = 60 meters
Finally, we can find the area of the field:
Area = Length * Breadth
Area = 80 * 60
Area = 4800 square meters
Therefore, the area of the rectangular field is 4800 square meters.
To find the area of the rectangular field, we need to determine its length and breadth.
Let's start by assigning variables to the length and breadth of the field. Let L represent the length and B represent the breadth.
The problem states that the breadth of the rectangular field is 75% of its length. Therefore, we can write an equation using this information:
B = 0.75L (Equation 1)
We also know that the diagonal of the rectangular field is 100 m. Using the Pythagorean theorem, we can relate the length, breadth, and diagonal of the field:
L^2 + B^2 = D^2 (Equation 2)
Now, substitute the value for B from Equation 1 into Equation 2:
L^2 + (0.75L)^2 = 100^2
Simplify the equation:
L^2 + 0.5625L^2 = 10000
Combine like terms:
1.5625L^2 = 10000
Divide both sides by 1.5625:
L^2 = 10000 / 1.5625
L^2 = 6400
Take the square root of both sides:
L = √6400
L ≈ 80
Now that we have the length, we can substitute this value back into Equation 1 to find the breadth:
B = 0.75L
B = 0.75 * 80
B = 60
So, the length is approximately 80 m and the breadth is 60 m.
Finally, we can calculate the area of the field:
Area = Length * Breadth
Area = 80 * 60
Area = 4800 m^2
Therefore, the area of the rectangular field is 4800 square meters.