All categories

3 years ago

a rectangle has an area of 320 feet squared. the length is 4 feet longer than the width. find the dimensions.

Mathematics

1 answer:

deff fn [24]3 years ago

4 0

Width of the rectangle is 16 ft and length of the rectangle is 20 ft

Step-by-step explanation:

Step 1:

Given area of the rectangle = 320 ft². Let the width of the rectangle be x, then the length = x + 4. Use the formula for area of a rectangle = (length × width)

320 = x(x + 4)

320 = x² + 4x

x² + 4x - 320 = 0

x = (-b ±√b² - 4ac)/2a = (-4 ±√16 - 4×1×-320)/2

= (-4±√1296)/2 = (-4 ± 36)/2

= 32/2, -40/2 = 16, -20 (neglecting the negative value)

∴ Width of the rectangle = 16 ft

∴ Length of the rectangle = 16 + 4 = 20ft

You might be interested in

At an airport , it costs $7 to park for up to one hour and $5 per hour for each additional hour. Let x represent the number of h

avanturin [10]

C(x) = 5x + 2

This is because at 1 hour it only cost 7 dollars, so it should only have 2 added to the end.

5 0

3 years ago

Margie needs to know the square footage for the first floor of the condo her client wants to make an offer on. The kitchen is 10

irga5000 [103]

Answer:

D. 850 square foot

Step-by-step explanation:

Area of a space is the length

multiply by the width

The area for the kitchen, dining, office and sunroom will be calculated independently and added together.

Note the word "and the office and sunroom are each 10 feet by 10 feet"

Kitchen area = 10 ft x 15ft= 150sqft

Living/Dining area = 20ftx25ft= 500sqft

Sunroom = 10ftx10ft= 100sqft

Office= 10ftx10ft=100sqft

Therefore total surface area is the cumulative of the 4 areas

150sqft+500sqft+100sqft+100sqft= 850sqft

8 0

3 years ago

Read 2 more answers

Solve this simultaneous equation x+2y=11 x-2y=1

lana [24]

Answer:

Equation 1,

$x + 2y = 11$

Equation 2,

$x - 2y = 11$

Take equation number 2.

$x - 2y = 11 \\ x = 11 + 2y$

Substitute 'x' in Equation number 1.

$x + 2y = 11 \\ 11 + 2y + 2y = 11 \\ 11 + 4y = 11 \\ 4y = 11 - 11 \\ 4y = 0 \\ y = \frac{0}{4} \\ y = 0$

y = 0.

So x,

$x = 11 - 2y \\ x = 11 - 2(0) \\ x = 11 - 0 \\ x = 11$

x = 11.

7 0

3 years ago

Read 2 more answers

A cafe stores ice cream in a large hemisphere-shaped bowl with a diameter of 36 cm.

skelet666 [1.2K]

Answer:

1115.8

Step-by-step explanation:

3 0

2 years ago

State whether the following coordinates on a Cartesian plane form an acute, obtuse or right triangle: a) (-1, 1), (7,-2) and (1,

LiRa [457]

Answer:

a) Acute triangle

b) Right triangle

Step-by-step explanation:

∵ A triangle having sides a, b and c is called,

Acute : If a² + b² > c² or a² + c² > b² or b² + c² > a²,

Obtuse : if a² + b² < c² or a² + c² < b² or b² + c² < a²

Right : a² + b² = c² or a² + c² = b² or b² + c² = a²,

a) Let A≡(-1, 1), B≡(7,-2) and C≡(1,-5),

By the distance formula,

$AB=\sqrt{(7-(-1))^2+(-2-1)^2}=\sqrt{(7+1)^2+(-3)^2}=\sqrt{8^2+3^2}=\sqrt{64+9}=\sqrt{73}\text{ unit}$

Similarly,

$BC=\sqrt{45}\text{ unit}$

$CA=\sqrt{40}\text{ unit}$

∵ The sum of any two sides is greater than third side,

So, ABC is a triangle,

Now,

$AB^2 + BC^2 > CA^2$

⇒ ABC is an acute triangle.

b) Let P≡(0,6), Q≡(1,2) and R≡(5,3),

By the distance formula,

PQ = √17 unit,

QR = √17 unit,

RP = √34 unit,

∵ The sum of any two sides of PQR is greater than third side,

⇒ PQR is a triangle ,

Also,

$RP^2=PQ^2+QR^2$

Hence, PQR is a right triangle.

3 0

3 years ago