in a rectangular field adjacent sides differ by 17 cm.its diagonal length is 25 cm.find the cost of fencing the field at rs 5 per metre
s^2 + (s+17)^2 = 25^2
s = 8
The field is 8x17 cm
What a tiny field!
cost is thus 2(8+17)cm * rs5/m * 1m/100cm = rs 2.5
How odd: since a=8,b=17
a+b = √(a^2+b^2)
My bad. I was thinking of an 8-15-17 triangle.
s=7
2(7+25)*5/100 = rs 3.20
rats! still bad arithmetic
7+17=24, not 25
you fix it
To find the cost of fencing the field, we need to calculate the perimeter of the rectangular field.
Let's start by solving the given information step by step:
1. We know that the adjacent sides of the rectangular field differ by 17 cm. Let's call the length of one side x.
The other side will then be x + 17 cm.
2. We are also given the diagonal length, which is 25 cm. We can use the Pythagorean theorem to relate the sides and the diagonal of a rectangle:
According to Pythagorean theorem, the square of the diagonal is equal to the sum of the squares of the sides.
So, we have (x^2) + (x+17)^2 = 25^2.
3. Expanding and simplifying the equation:
x^2 + (x^2 + 34x + 289) = 625.
Combining like terms:
2x^2 + 34x + 289 = 625.
Rearranging terms:
2x^2 + 34x - 336 = 0.
4. To find the values of x, we can solve this quadratic equation. We can either factorize it or use the quadratic formula.
In this case, factoring is not straightforward, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a).
For the given equation, a = 2, b = 34, and c = -336.
x = (-34 ± √(34^2 - 4 * 2 * -336)) / (2 * 2).
Simplifying further:
x = (-34 ± √(1156 + 2688)) / 4.
x = (-34 ± √(3844)) / 4.
x = (-34 ± 62) / 4.
This gives two possible solutions for x: x = 7 (taking a positive square root), or x = -23.75 (taking a negative square root). Since length cannot be negative, we discard x = -23.75.
5. So, the length of one side of the rectangular field is 7 cm. The other side will be 7 + 17 = 24 cm.
6. Now, let's calculate the perimeter of the rectangular field:
Perimeter = 2(length + width).
Perimeter = 2(7 + 24) cm.
Perimeter = 62 cm.
7. To calculate the cost of fencing the field at Rs 5 per meter, we need to convert the perimeter from centimeters to meters:
Perimeter in meters = 62 cm ÷ 100.
Perimeter in meters = 0.62 meters.
8. Finally, we can calculate the cost of fencing the field:
Cost = Perimeter in meters * Cost per meter.
Cost = 0.62 meters * Rs 5.
Cost = Rs 3.10.
Therefore, the cost of fencing the field at Rs 5 per meter would be Rs 3.10.