Answer:
Real-life problem:
A farmer has a rhombus-shaped field with a side length of 50 meters and a height of 30 meters. He wants to build a fence around the field to keep his cows from wandering off. If he plans to use wire fencing that costs $4 per meter, how much will he spend on fencing?
Solution:
To find the perimeter of the field, we need to calculate the length of each side. Since a rhombus has four equal sides, we can use the Pythagorean theorem to find the length of each side:
a^2 + b^2 = c^2
where a and b are the side lengths, and c is the diagonal.
Since the height of the rhombus is 30 meters and the side length is 50 meters, we can use these values to find the diagonal:
c^2 = 30^2 + 50^2
c^2 = 900 + 2500
c^2 = 3400
c = sqrt(3400)
c = 58.31 meters
Therefore, the perimeter of the field is 4 x 50 = 200 meters.
The farmer plans to use wire fencing that costs $4 per meter. So, the total cost of fencing will be:
Cost = perimeter x cost per meter
Cost = 200 x 4
Cost = $800
Answer:
The farmer will spend $800 on fencing the rhombus-shaped field.