The parallel edges of a trapezium shaped field are 77m and 60m.If the remaining edges are 25M and 26m,what is the total cost of digging twice the land at the rate of Rs.10 persq m and fencing thr land three times at the rate of Rs.20 per m
Ans
From each of the ends of the 60 m side, draw altitudes to the 77 m side.
You now have a rectangle and two right-angled triangles.
Let the height of all three be h,
for the triangle with hypotenuse 25, let the base be x, then
x^2 + h^2 = 25^2 -----> h^2 = 625 - x^2
for the triangle with hypotenuse 26, let the base be 10-x
h^2 + (10-x)^2 = 26^2 ---> h^2 = 376 - (10-x)^2
625 - x^2 = 376 - (10-x)^2
a bit of simple algebra yields:
x = 49/20 = 2.45 m
now you can find the base of the other triangle , 10-x
and the height h
All is now known, and you can find area, perimeter or whatever else you need.
To find the total cost of digging and fencing the trapezium-shaped field, we need to calculate the area of the field and then multiply by the respective costs per square meter and per meter.
Step 1: Find the height of the trapezium:
Since the trapezium has parallel edges, we can use the formula for the area of a trapezium:
Area = (a + b) * h / 2
Where a and b are the parallel edges, and h is the height.
In this case, the parallel edges are 77m and 60m.
Area = (77m + 60m) * h / 2
Step 2: Solve for the height:
We need to calculate the height of the trapezium.
Using the given lengths of the remaining edges (25m and 26m), we can create two equations:
25m = (77m + 60m) * h / (77m - 60m)
26m = (77m + 60m) * h / (77m + 60m)
Now we can solve these equations to find the value of h.
Step 3: Calculate the area:
Once we have the height, we can substitute it into the area formula to find the area of the trapezium.
Area = (77m + 60m) * h / 2
Step 4: Calculate the total cost of digging:
To find the total cost of digging twice the land at the rate of Rs.10 per square meter, we multiply the area by the cost.
Total cost of digging = 2 * Area * Rs.10
Step 5: Calculate the total cost of fencing:
To find the total cost of fencing the land three times at the rate of Rs.20 per meter, we need to find the perimeter of the trapezium.
Perimeter = 77m + 60m + 25m + 26m
Total cost of fencing = 3 * Perimeter * Rs.20
Step 6: Calculate the total cost:
Finally, to find the total cost, we add the cost of digging and the cost of fencing.
Total cost = Total cost of digging + Total cost of fencing
To find the total cost of digging and fencing the field, we need to calculate the area of the trapezium-shaped field first. The formula for the area of a trapezium is:
Area = (sum of parallel sides / 2) * height
In this case, the sum of the parallel sides is 77m + 60m = 137m, and the height can be calculated by subtracting the smaller base from the larger base: 60m - 26m = 34m.
Plugging these values into the formula, we find:
Area = (137m / 2) * 34m
Area = 68.5m * 34m
Area = 2329 sq m
Next, we need to calculate the cost of digging twice the land at the rate of Rs.10 per sq m. This can be done by multiplying the area by the cost per sq m:
Cost of digging = Area * Cost per sq m
Cost of digging = 2329 sq m * Rs.10/sq m
Cost of digging = Rs. 23,290
Now, let's calculate the cost of fencing the land three times. The perimeter of the trapezium can be found by adding up all the sides: 77m + 60m + 25m + 26m = 188m.
Next, we multiply the perimeter by the cost per meter of fencing:
Cost of fencing = Perimeter * Cost per meter
Cost of fencing = 188m * Rs.20/m
Cost of fencing = Rs. 3,760
Finally, to find the total cost, we add the cost of digging and the cost of fencing:
Total cost = Cost of digging + Cost of fencing
Total cost = Rs. 23,290 + Rs. 3,760
Total cost = Rs. 27,050
Therefore, the total cost of digging twice the land and fencing the land three times is Rs. 27,050.