Question

max needs to purchase a new sail for his boat. the dimensions of the sail are shown in the diagram. the sail will cost $3.25 per square foot. how much will max pay for the sail?

Answer 1

`\text{ \$176.41}`

Step-by-step explanation

We want to find the total cost of the sail for the boat.

To do this, we have to find the area of the sail and then find the product of the area and the cost per sqare foot.

To find the area of the triangle, we apply:

`\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ s=(a+b+c)/(2) \\ a,b,c\text{ are sides of the triangle} \end{gathered}`

Therefore, we have that:

`\begin{gathered} s=(16(3)/(4)+17(1)/(2)+6(1)/(2))/(2) \\ s=(40(3)/(4))/(2) \\ s=20.375ft \end{gathered}`

Therefore, we have that the area is:

`\begin{gathered} A=\sqrt[]{20.375(20.375-16.75)(20.375-17.5)(20.375-6.5)} \\ A=\sqrt[]{20.375\cdot3.625\cdot2.875\cdot13.875} \\ A=\sqrt[]{2946.3} \\ A=54.28ft^2 \end{gathered}`

Now, we have to find the cost of the sail:

`\begin{gathered} \text{Cost}=54.28\cdot3.25 \\ \text{Cost}=\text{ \$176.41} \end{gathered}`

That is how much it would cost.