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

HELP ME PLSSSSSS!!!!!!!

n200080 [17]

Answer:

1) $m\angle x = 35^{\circ}$ , 2) $m\angle x = 60^{\circ}$ , 3) $m \angle x = 40^{\circ}$

Step-by-step explanation:

1) Triangle is a right triangle since tangent line is perpendicular to the radius of the circle. Based on the fact that the sum of internal angles in triangles equals 180°, we find the value of the angle $x$ :

$m\angle x = 180^{\circ} - 90^{\circ} - 55^{\circ}$

$m\angle x = 35^{\circ}$

2) Both triangles are symmetrical right triangles since tangent lines are perpendicular to the two radii and common side is parallel to the third radius. Based on the fact that the sum of internal angles in triangles equals 180°, we find the value of the angle $x$ :

$m \angle x = 180^{\circ} - 90^{\circ} - 30^{\circ}$

$m\angle x = 60^{\circ}$

3) The figure is formed by two symmetrical right triangles. These triangles are right-angled and symmetrical since tangent lines are perpendicular to the two radii and common side is parallel to the third radius. Based on the fact that the sum of internal angles in quadrilaterals equals 360°, we find the value of the angle $x$ :

$m\angle x = 360^{\circ} - 180^{\circ} - 140^{\circ}$

$m \angle x = 40^{\circ}$

4 0

3 years ago

What times 5/8 equals 1

nydimaria [60]

Answer:

1.6

Step-by-step explanation:

5/8 = .625

1/.625 = 1.6

.625* 1.6 = 1

8 0

3 years ago

Read 2 more answers

Ratio of 12 seconds to 1 hour

kodGreya [7K]

12:3600

1:300

I edited it lol

hope that helps

6 0

3 years ago

Please help me to understand how to explain the steps when solving 3(n + 5) ≥ 3n + 8.

chubhunter [2.5K]

Answer:

0 ≥ -7

Step-by-step explanation:

3(n + 5) ≥ 3n + 8

3n + 15 ≥ 3n + 8

3n - 3n ≥ 8 - 15

0 ≥ -7

3 0

3 years ago

Tom's Sports Wear is a retailer of sports hats located in Atlanta, Georgia. Although Tom's carries numerous styles of sports hat

Kaylis [27]

The annual breakeven point is $550157

Given that the Sales price is $ 31.00, Per-unit variable costs: Invoice cost is 17.05, Sales commissions is 4.05, Total per-unit variable costs is $ 21.10, Total annual fixed costs: Advertising is $ 23,100, Rent is 28,200, Salaries is 124,200 and Total fixed costs is $ 175,500.

The break-even point is your total fixed cost divided by the difference between the unit price and the variable cost per unit.

The sales price is $31 and the total variable cost is $21.10.

Now, we will find the Contribution margin by subtracting the Total variable cost from the sales price, we get

Contribution margin= Sales price-Total sales price

Contribution margin=31-21.10

Contribution margin=9.9

Further, we will find the contribution margin ratio by dividing the contribution margin by Sales price, we get

contribution margin ratio=contribution margin/Sales price

contribution margin ratio=9.9/31

contribution margin ratio=0.319

contribution margin ratio=31.9%

Furthermore, we will find the break-even point, we get

Break-even point=Fixed cost/contribution margin

Break-even point=175500/9.9

Break-even point=17727.27

Now, we will find the break-even sales in dollars, we get

Break-even sales=Fixed cost/contribution margin ratio

Break-even sales=(175500/31.9)×100

Break-even sales=550157

Hence, the annual breakeven point in unit sales is calculated to be $550157.

Learn more about the break-even point from here brainly.com/question/10573173.

#SPJ1

5 0

2 years ago