Asquare has a side length of x. a rectangle has a length that is 4 inches longer than the square and a width that is 2 inches shorter than the square. if the areas of the square and rectangle are equal, what is the length of the rectangle?

Length of the rectangle is = 8 inches.

Step-by-step explanation:

Given :

Area of square = Area of the rectangle

According to the question:

Length of the square be 'x'.

Its area = (Side)*(Side) =   ...equation (i)

Length of the rectangle =

Width of the rectangle =

Area of the rectangle =Length * Width

⇒

⇒          ...equation  (ii)

Equating both the equation as area of both the figure are equal.

⇒

⇒     ...subtracting both sides

⇒           ...dividing both sides with 2

⇒ inches

Plugging the value of x=4 in the length of the rectangle.

We have,

⇒

So the length of the rectangle = 8 inches.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.