Question

Mia is decorating a ballroom ceiling with garland. If the rectangular ceiling is 63 feet by 60 feet, how much garland will Mia need to reach from one corner of the ceiling to the opposite corner?

Answer 1

Given the dimensions of the rectangular ceiling below

`\begin{gathered} \text{length}=63\text{feet} \\ \text{width}=60\text{feet} \end{gathered}`

Let us sketch out the image of the rectangle ceiling.

We are to solve for x, which represents the cost of garland Mia will need to reach from one corner of the ceiling to the opposite corner.

Let us now sketch out the triangular shape from the rectangle.

Using Pythagoras theorem to solve for x,

Therefore,

`\begin{gathered} x^2=60^2+63^2 \\ x^2=3600+3969 \\ x^2=7569 \\ x=\sqrt[]{7569} \\ x=87\text{feet} \\ \therefore x=87feet \end{gathered}`

Hence, the cost of garland Mia will need to reach from one corner of the ceiling to the opposite corner is 87feet.