A piece of property in downtown Huston is advertised for sale at $45 per square foot. If the lengths of the sides of the triangular lot are 220 feet, 234 feet, and 160 ft, then what is the asking price for the lot?

1 Answer
MJ
Jan 2, 2018

Asking price for the lot is #$761836.05#

Explanation:

To find the cost of the triangular plot, we need to know the area. How to know if we need to find the area or perimeter is based on the price which is given in per square foot. square foot is the measure of area, so we need to find the area of the triangle first.

To find the area of the triangle, when 3 sides are given is done by using Heron's formula:

Area = #sqrt(p(p-a)(p-b)(p-c)#
Where, #p# = perimeter = #(a+b+c)/2#,
and #a,b,c# are the three sides of the triangle.

So, #p# = #(220+234+160)/2# = #307 feet#

Now, putting all values in Heron's formula:

Area = #sqrt(307xx(307-220)xx(307-234)xx(307-160)#

or, Area = #sqrt(307xx87xx73xx147# = #sqrt(286614279)#

or Area = #16929.69# sq. feet

Now cost of 1 square foot = #$45#
Therefore, cost of #16929.69# sq. feet = #45xx16929.69#=#$761836.05#

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