Maximizing areaof3 sidedenclosuresslidedeck

What is the maximum 3-sided rectangular area we can enclose given 100 m of rope?

@MathletePearcewww.tapintoteenminds.com

Perimeter =

A SQUARE WILL ALWAYS MAXIMIZE AREA OF 4-SIDED

ENCLOSURES

25 m 25 m

25 mPerimeter =

25 m 25 m

25 mPerimeter =

5 m 5 m90 m

Area = (90 m)(5 m)

5 m 5 m90 m

Area = 450 m25 m 5 m450 m2

5 m 5 m90 m

Width Area

Area = 450 m2450 m25 m 5 m

5 m 5 m90 m

Width Area

Area = 450 m2

450 m25 m5 m

Width Area

450 m25 m5 m

Width Area

450 m25 m5 m15 m 15 m

Width Area

Area = 1,050 m2

450 m25 m5 m15 m 15 m1,050 m215 m 15 m

Width Area

Area = 1,050 m2

450 m25 m5 m15 m 15 m1,050 m215 m15 m

Width Area

450 m25 m5 m1,050 m215 m15 m25 m

25 m 25 m

3 sides

25 m 25 m

3 sides= 8.3 m8.3 m8.3 m8.3 m

25 m 25 m

3 sides=

8.3 m8.3 m8.3 m

25 m 25 m

3 sides=

25 m 25 m

3 sides= 8.3 m

8.3 m8.3 m

33.3 m 33.3 m

33.3 m

3 sides= 8.3 m

33.3 m 33.3 m

33.3 m

1,108.9 m21,108.9 m2 =33.3 m 33.3 m

Width Area

450 m25 m5 m1,050 m215 m15 m

Width Area

450 m25 m5 m1,050 m215 m15 m

33.3 m 33.3 m

33.3 m

1,108.9 m2

1,108.9 m2 =

33.3 m33.3 m

25 m 25 m

Area = (25 m)(25 m)

25 m 25 m

Area =

Area =(25 m)(25 m) (25 m)(25 m)

25 m 25 m

Area = 625 m2

25 m 25 m

25 m25 m

= 625 m2

Area = 625 m2

Area25 m 25 m

25 m 25 m25 mAreaArea

= 1,250 m225 m 25 m1,250 m2

Width Area

450 m25 m5 m1,050 m215 m15 m1,108.9 m233.3 m

25 m 25 m25 mAreaArea

25 m = 1,250 m21,250 m2

Width Area

450 m25 m5 m1,050 m215 m15 m

1,108.9 m233.3 m

25 m 25 m

Area = 1,250 m2

1,250 m225 m

Width Area

450 m5 m5 m1,050 m15 m15 m

1,108.9 m33.3 m

25 m 25 m

Area = 1,250 m

1,250 m225 m

MAKE A SQUARE AND

DOUBLE THE LENGTH

TO MAXIMIZE AREA OF

3-SIDED ENCLOSURES

What is the maximum 3-sided rectangular area we can enclose given of rope?

50 mMAKE A SQUARE AND

DOUBLE THE LENGTH

TO MAXIMIZE AREA OF

3-SIDED ENCLOSURES

50 m 50 m

MAKE A SQUARE AND

DOUBLE THE LENGTH

TO MAXIMIZE AREA OF

3-SIDED ENCLOSURES

50 m 50 m

MAKE A SQUARE AND

DOUBLE THE LENGTH

TO MAXIMIZE AREA OF

3-SIDED ENCLOSURES

50 m 50 m = 5,000 m2Area

MAKE A SQUARE AND

DOUBLE THE LENGTH

TO MAXIMIZE AREA OF

3-SIDED ENCLOSURES

Maximizing areaof3 sidedenclosuresslidedeck

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