Question

The plan of a terrace is shown at right. The scale is 2 inches : 6 feet. What are the length and width of the terrace? Find the area

Answer 1

Part 1) The length of the terrace is
`15\ ft`

Part 2) The width of the terrace is
`6\ ft`

Part 3) The area of the terrace is
`90\ ft^(2)`

Explanation:

we know that

The scale of the plan is
`(2)/(6) (in)/(ft)`

see the attached figure to better understand the problem

Step 1

Find the length of the terrace

we know that

The length of a terrace in the plan is equal to
`5\ in`

so

by proportion

Find the length of the terrace in the actual

`(2)/(6) (in)/(ft)=(5)/(x) (in)/(ft)\\ \\x=6*5/2\\ \\x=15\ ft`

Step 2

Find the width of the terrace

we know that

The width of a terrace in the plan is equal to
`2\ in`

so

by proportion

Find the width of the terrace in the actual

`(2)/(6) (in)/(ft)=(2)/(x) (in)/(ft)\\ \\x=6*2/2\\ \\x=6\ ft`

Step 3

Find the area of a terrace

we know that

The area of a terrace is equal to

`A=LW`

we have

`L=15\ ft`

`W=6\ ft`

substitute

`A=15*6=90\ ft^(2)`