Q. 55 - Precalculus Enhanced with Graphing Utilities

Question

The perimeter of a rectangular floor is 90 feet. Find the

dimensions of the floor if the length is twice the width.

Step-by-Step Solution

Answer

The dimension of the rectangular floor is 30 feet , 15 feet

Step 1: Given information

Perimeter of rectangular floor is 90 feet and length is as twice as breadth

Step 2: Write the formula for perimeter and simplify

Perimeter of rectangle can be given as $2(l+b)$ Where $l=length,b=breadth$

Hence

$$\begin{gathered} 2(l+b)=90 \\ l+b=45 \end{gathered}$$                 (1)

also we are given that length of the rectangle is as twice as breadth

hence $l=2b \left(2\right)$

Substituting 2 in 1 we get

$$\begin{gathered} l+b=45 \\ 2b+b=45 \\ 3b=45 \\ b=15feet \end{gathered}$$

Now we find the length

$$\begin{gathered} l=2b \\ l=2\left(15\right) \\ l=30feet \end{gathered}$$

Step 3: Conclusion

The length and breadth of the rectangular floor is $30feet, 15 feet$