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A rectangle has width that is 6 meters less than the length. The area of the rectangle is 280 square meters. Find the dimensions

salantis [7]

Dimensions are length 20 meter and width 14 meter

Solution:

Let "a" be the length of rectangle

Let "b" be the width of rectangle

Given that,

A rectangle has width that is 6 meters less than the length

Width = length - 6

b = a - 6

The area of the rectangle is 280 square meters

The area of the rectangle is given by formula:

$Area = length \times width$

Substituting the values we get,

$Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0$

Solve the above equation by quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}$

$a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14$

Since, length cannot be negative, ignore a = -14

Thus solution of length is a = 20

Therefore,

width = length - 6

width = 20 - 6 = 14

Thus dimensions are length 20 meter and width 14 meter

6 0

4 years ago

As an airplane rises, the outside temperature drops 3.6 degrees Fahrenheit for each 1000 feat of elevation gain. Suppose the out

VLD [36.1K]

Answer:

30000 feet

Step-by-step explanation:

temperature on ground level = 65 °F

temperature at cruising altitude = -43 °F

total decrease in temperature = 65 - (- 43) = 65 + 43 = 108 °F

for each 1000 feet elevation temperature drops by 3.6 °F

and we have the total drop of temperature as 108 °F.

so, Height of plane at cruising altitude = (drop in temperature/ 3.6) X 1000

= $\frac{108}{3.6} X 1000$

= 30000 feet

7 0

4 years ago

For the following problem state the objective function and the constraints. DO NOT solve:

Mama L [17]

Answer:

If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit P can be expressed as:

$P=3S+5H$

The restriction for cloth can be written as:

$S+2H\leq500$

The restriction for metal can be written as:

$2S+3H\leq600$

The restriction for wood can be written as:

$4S+7H\leq800$

The condition for S and H to be positive is:

$S, H \geq0$

Step-by-step explanation:

We have an objective function that, in this case, we want ot maximize.

This function is the Profit (P).

If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit can be expressed as:

$P=3S+5H$

We have 3 restrictions, plus the condition that both S and H are positive.

The restriction for cloth can be written as:

$S+2H\leq500$

The restriction for metal can be written as:

$2S+3H\leq600$

The restriction for wood can be written as:

$4S+7H\leq800$

The condition for S and H to be positive is:

$S, H \geq0$

5 0

3 years ago

In a particular year, the United States had a national debt of 1.1 x 1013 U.S. dollars.

kolezko [41]

The answer is to your question is 100:1

4 0

3 years ago

While playing a video game a player collected 18 of the 45 available coins right and simplify a fraction to represent the situat

Tema [17]

Answer:

2 / 5

Step-by-step explanation:

Fractions are written in the form part/whole, in this case, the part is 18 and the whole is 45 so the fraction would be 18 / 45 which simplifies to 2 / 5.

7 0

4 years ago