Question

Gloria is digging for fossils at a geological site. She has 120 meters of rope and 4 stakes to mark off a rectangular area. Which set of dimensions will create a rectangle using all the rope Gloria has with her? 12 m × 10 m 50 m × 10 m 60 m × 60 m 45 m × 10 m

Answer 1

Answer:

50 m × 10 m

Step-by-step explanation:

There is a total of 120 meters of rope.  This is the distance around, so this is perimeter.

Perimeter is found by adding together the lengths of all sides of a figure.  This means all 4 sides added together must make 120.

For our first choice, 12 by 10, we would have two sides that are equal to 12 and 2 sides that are equal to 10.  This gives us a perimeter of

12+12+10+10 = 44

This is not 120, so this is not the correct choice.

For the second choice, 50 by 10, we have two sides that are equal to 50 and 2 sides that are equal to 10.  This gives us a perimeter of

50+50+10+10 = 120

This is the correct choice.

For the third choice, 60 by 60, we have all four sides equal to 60.  This gives us a perimeter of

60+60+60+60 = 240

This is not 120, so this is not the correct choice.

For the last choice, 45 by 10, we have two sides that are equal to 45 and 2 sides that are equal to 10.  This gives us a perimeter of

45+45+10+10 = 110

This is not 120, so this is not the correct choice.

Answer 2

The correct answer is option B. 50m × 10m

What is rectangle?

"A rectangle is a quadrilateral in which all the angles are equal (90°) and the opposite sides are equal and parallel. "

From given data,

Gloria has a rope of 120m and 4 stakes to mark rectangular area.

The perimeter of rectangle = the length of the rope

This means, we need to find the dimension of rectangle such that perimeter will be 120m.

Formula to calculate the perimeter of rectangle:

Let $P,l,w$ represents the perimeter, length and width of the rectangle respectively.

$P=2(l+w)$

For the first dimension 12m × 10m,

⇒ $P=2(12+10)$

⇒ $P=44$ m which is not equal to 120m

Consider the second dimension 50m × 10m

⇒ $P=2(50+10)$

⇒ $P=120$m

Consider the third dimension 60m × 60m

⇒ $P=2(60+60)$

⇒ $P=240$m

Consider the last dimension 45m × 10m

⇒ $P=2(45+10)$

⇒ $P=110$ m

Hence, the correct answer is option B. 50m × 10m

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