Question

The real estate term lake frontage refers to the distance along the edge of a piece of property that touches a lake.

Find the lake frontage (to the nearest tenth) of each lot shown.
A:
B:
C:

Suppose that lot prices are in the same ratio as lake frontages. The least expensive lot is $250,000. Use your rounded values from part (a) to find the prices of the other lots. Round your answers to the nearest thousand dollars.
The prices of the other lots, from least to greatest, are $__ and $__.

Answer 1

Part a) The lake frontage of lot A is
`50.9\ yd`

Part b) The lake frontage of lot B is
`58.4\ yd`

Part c) The lake frontage of lot C is
`64.7\ yd`

Part d) The prices of the other lots, from least to greatest, are
`\$286,836.94` and
`\$317,779.96`

Explanation:

we know that

If two figures are similar, then the ratios of its corresponding sides is equal

Find the lake frontage (to the nearest tenth) of each lot shown

we have that

`(174)/((48+55+61))=(A)/(48)=(B)/(55)=(C)/(61)`

`(174)/(164)=(A)/(48)=(B)/(55)=(C)/(61)`

step 1

Find the lake frontage of lot A

`(174)/(164)=(A)/(48)`

`A=174*48/164=50.9\ yd`

step 2

Find the lake frontage of lot B

`(174)/(164)=(B)/(55)`

`B=174*55/164=58.4\ yd`

step 3

Find the lake frontage of lot C

`(174)/(164)=(C)/(61)`

`C=174*61/164=64.7\ yd`

step 4

Find the prices of the other lots

we know that the price of the lot A is
`\$250,000` (given problem)

so

by proportion

`(\$250,000)/(50.9)=(\$B)/(58.4)=(\$C)/(64.7)`

Find the price lot B

`(\$250,000)/(50.9)=(\$B)/(58.4)`

`B=250,000*58.4/50.9=\$286,836.94`

Find the price lot C

`(\$250,000)/(50.9)=(\$C)/(64.7)`

`C=250,000*64.7/50.9=\$317,779.96`

The prices of the other lots, from least to greatest, are
`\$286,836.94` and
`\$317,779.96`