A rectangle has sides of #(7 + sqrt2)# feet and #(7 - sqrt2)# feet long. What is the area and the perimeter of the rectangle?

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Answer 1 · 2015-12-01T02:47:33

#P=28#
#A=47#

Perimeter:

The rectangle's sides are #(7+sqrt2),(7+sqrt2),(7-sqrt2),# and #(7-sqrt2)#.

To find the perimeter, we add all of these to one another:

#(7+sqrt2)+(7+sqrt2)+(7-sqrt2)+(7-sqrt2)#

We can rearrange the order to see that the perimeter equals:

#7+7+7+7+sqrt2-sqrt2+sqrt2-sqrt2#

Notice that all the square root terms will cancel, and the sevens will add together for a perimeter of 28.

Area:

To find the area of the rectangle, multiply the base length by the height length. We will have to FOIL.

#(7+sqrt2)(7-sqrt2)=49-7sqrt2+7sqrt2-2#

Two things: notice that #sqrt2xx-sqrt2=-2# and that the #7sqrt2# terms will cancel.

This leaves us with an area of #49-2# or 47.