basic geometry

[poltrock]

The area of a triangle is 100 square inches.The perimeter of the rectangle is 40 inches. A second rectangle has the same area but a different perimeter. Is the second rectangle a square? explain why or why not. that is the question as stated. Also is it possible to have a perimeter of 40 inches and have an area of 100 inches.

 

[Ishuda]

The area of a triangle is 100 square inches.The perimeter of the rectangle is 40 inches. A second rectangle has the same area but a different perimeter. Is the second rectangle a square? explain why or why not. that is the question as stated. Also is it possible to have a perimeter of 40 inches and have an area of 100 inches.

You have mixed types "The area of a triangle is 100 square inches.The perimeter of the rectangle is 40 inches." However, assuming a rectangle in both cases, if p is the perimeter and a is the area then \(\displaystyle a\, \le\, (\frac{p}{4})^2\). Since \(\displaystyle 100\, \le\, (\frac{40}{4})^2 = 100\), yes, a rectangle can have a perimeter of 40 inches and have an area of 100 inches.

 

[Ishuda]

The area of a triangle is 100 square inches.The perimeter of the rectangle is 40 inches. A second rectangle has the same area but a different perimeter. Is the second rectangle a square? explain why or why not. that is the question as stated. Also is it possible to have a perimeter of 40 inches and have an area of 100 inches.

HINT: If x is one side of a rectangle and y is the other side, what is the formula for the perimeter? What is the formula for the area. Given those two equations, how would you solve for the two variables?

 

[poltrock]

sorry the post at 6:49 pm is the correct question the triangle should be rectangle, apologize.

 

[poltrock]

the question is as stated in Common core reteaching and practice, Envision math common core, but the question has no other available info.

 

[poltrock]

The question is not triangle I must have made a mistake it should be rectangle, very much apologize.

 

[Ishuda]

The question is not triangle I must have made a mistake it should be rectangle, very much apologize.

Look at the hint above (or below, depending on how you have set your preferences) and show us what you have done.

 

[Ishuda]

I see the formula as written 40 over 4 squared =100 but, can that happen in 2 dimensional space.

Start over. Given x as width and y as the length of a rectangle what are the formulas for the perimeter and area?

Answer:
perimeter = 2 (x+y)
area = x * y

Now if the area is 100 and the perimeter is 40, what are x and y?

 

[poltrock]

new geometry

it would the answer is 10.

 

[Ishuda]

it would the answer is 10.

Correct x=y=10, so the rectangle is a square.

Now suppose a second rectangle has the same area (100) but a different perimeter. Since the area is the same, from the formula above, \(\displaystyle a\, \le\, (\frac{p}{4})^2\, or\, 4\, \sqrt{a}\, \le\, p\), we have that the perimeter has to be larger than 40. So let the perimeter be 40 + 2d where d is positive and we have
x + y = 20 + d
x y = 100.
What is x and y? Are they the same? If not, the rectangle is not a square. From this can you give a formula of the perimeter in terms of the area (or area in terms of the perimeter) given that the rectangle is a square?