Question

Hello I was just wondering if this is the correct solution to this question and if not what is the correct solution?

Answer 1

A garden is given to have the shape of a right triangle with a hypothenuse length of 7m and a leg of length 5m. It is required to find the total cost of fencing if fencing cost $2.50/m.

To do this, find the missing length of leg, calculate the perimeter of the garden, and then multiply the perimeter by the cost of fencing per meter.

Recall the Pythagorean Theorem:

`a^2+b^2=c^2`

Where a and b are the lengths of the legs of the right triangle, and c is the length of the hypothenuse.

Let the missing length be b.

Substitute a=5 and c=7 into the equation:

`5^2+b^2=7^2`

Solve the equation for b:

`\begin{gathered} 25+b^2=49 \\ \Rightarrow b^2=49-25 \\ \Rightarrow b^2=24 \\ \Rightarrow b=√(24)\approx4.9 \end{gathered}`

Next, find the Perimeter of the garden by adding the side lengths:

`a+b+c=5+4.9+7=16.9\text{ m}`

Multiply the perimeter by the cost per meter to get the total cost of fencing:

`16.9\cdot2.50=\$42.25`

The total cost of fencing is $42.25.