All categories

3 years ago

What is the largest possible area (in cm²) for a rectangle with a perimeter of 120 cm?

Mathematics

1 answer:

kompoz [17]3 years ago

8 0

Answer:

900 cm²

Step-by-step explanation:

Perimeter of a rectangle is given by

P=2(l+w)

Where l and w are length and width respectively.

Substituting P with 120 cm

120=2(l+w)

Divide both sides by 2

60=l+w

Making w the subject of formula

w=60-l

Area, A=lw

Substitute w with 60-l

A=l(60-l)=60l-l²

Since A=60l-l²

Get the first derivative of A with respect to l

0=60-2l

l=60/2=30

Therefore, w=60-l=60-30=30

The length abd width are both 30cm. This is a square and a square is also a type of rectangle since it has four sides.

Area=30*30=900cm²

You might be interested in

What is a mathematical phrase that includes at least one variable and one operation

sp2606 [1]

An expression.

Hope this helps :)

4 0

4 years ago

Read 2 more answers

Frank is having a raised rectangular platform built. He designed it so that the length of the platform is 4 feet longer than the

Anastaziya [24]

One system of equations would be
L = w+4
H = w-10
4H + 8(wL) = 1544
There is one viable solution; the width is 12, the length is 16, and the height is 2.

Using substitution with the system of equations, we have
4(w-10)+8(w(w+4))=1544
4w-40+8(w²+4w)=1544
4w-40+8w²+32w=1544

Combining like terms, we have
8w²+36w-40=1544

Factoring out a 4, we have
4(2w²+9w-10)=1544

Dividing both sides by 4 gives us
2w²+9w-10=386

Subtract 386 from both sides to get
2w²+9w-396=0

Using the quadratic formula, we have
$w=\frac{-9\pm \sqrt{9^2-4(2)(-396)}}{2(2)}
\\
\\=\frac{-9\pm \sqrt{81--3168}}{4}
\\
\\=\frac{-9\pm \sqrt{3249}}{4}=\frac{-9\pm 57}{4}
\\
\\=\frac{-9+57}{4}\text{ or }\frac{-9-57}{4}=\frac{48}{4}\text{ or }\frac{-66}{4}
\\
\\=12\text{ or }-16.5$

Since a negative width makes no sense, we know that w=12.

This means L=w+4=12+4=16 and H=w-10=12-10=2

5 0

4 years ago

25 POINTS, QUICKLY PLEASE!

Katarina [22]

Answer:

1) y > x² + 4x - 5, y > x + 5

2) Rational

Step-by-step explanation:

For a parabola, if the shade is inside the curve then the value of y will be greater or equal to:

For a line, if the shade is above it then the value of y will be greater or equal to:

Therefore, since parabola doesn't have solid curve (--- graph) then the inequality is ">"

Therefore, the inequality for parabola is y > x² + 4x - 5

For a line, it does not have solid graph so the inequality is ">"

Therefore, the inequality for line is y > x + 5

-----------

The graph of function describes the shape of rational function. It cannot be exponential as exponential only has one curve. It cannot be logarithm for same reason as exponential. It cannot be polynomial as polynomial is continuous function but the graph is discontinuous at specific point x = 0.

That being said, all choices except rational are all continuous function by default but rational function isn't and since the graph is discontinuous then we can say that it's rational function.

5 0

2 years ago

An iPhone that is marked $500 is marked up 250%.

belka [17]

Answer:

Step-by-step explanation:

This would be 500 x 250/100 = 125000/100 = 1250

8 0

3 years ago

Which planet is the third farthest away from the sun? Uranus Jupiter Saturn Neptune

svet-max [94.6K]

Answer:

saturn

Step-by-step explanation:

it goes Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune

8 0

3 years ago

Read 2 more answers