A backyard has a perimeter of 144 m.

If the backyard is square, what are the dimensions?

If the backyard is rectangular, and the length is three times the

width, what are the dimensions?

If the backyard is a triangle, as shown, write an algebraic expression for the perimeter and find its dimensions.

Which of the three backyard designs has the greatest area? Which has the least?

xRainexSiderisx
Mar 10, 2017

#1**+1 **

If the backyard is square, what are the dimensions?

perimeter = 4(length of one side)

144 = 4(length of one side)

36 m= length of one side

So the dimensions are 36 m by 36 m.

If the backyard is rectangular, and the length is three times the

width, what are the dimensions?

perimeter = 2(length + width)

144 = 2[3(width) + (width)]

144/2 = 3(width) + (width)

72 = 4(width)

18 m = width

length = 3(18) = 54 m

So the dimensions are 54 m by 18 m

I can't see the picture for the third one for some reason.

hectictar
Mar 10, 2017

#3**0 **

Square backyard: 36m by 36m.

Rectangular backyard: 18m by 54m.

Triangular backyard (even though it isn't shown, so going to assume it was a 45, 45, 90 triangle): 96m by 24m by 24m

Square backyard: 1296m^2

Rectangular backyard: 972m^2

Triangular backyard(had to take educational guess using heron's formula): Area≈1629.174023853805670541696m^2

Area greatest to least: Triangular backyard, Square backyard, Rectangular backyard.

2 things btw. One, post a link to the picture next time so that the answer to the triangular backyard is more accurate.

And two, its obvious that you copied and pasted this from an assignment of some sort, try and not rely on this website for that. Its better to learn on your own.

Guest Mar 10, 2017

#4**0 **

....and go ONE step further.....make the perimeter a CIRCLE to maximize the enclosed area......FWIW.

ElectricPavlov
Mar 10, 2017