Arectangle has an area of 24 sq. inches and a perimeter of 50 in. what are the dimensions of the rectangle

Length of rectangle = 24 inches

Width of rectangle = 1 inches

Step-by-step explanation:

Area of rectangle = 24 square inches

Perimeter of rectangle = 50 inches

Formulas:

Area of rectangle =

Perimeter of rectangle =

where represents length of rectangle and represents width of rectangle.

So, we can get two equations for and

A)    [Area]

B)     [ Perimeter ]

Simplifying equation B.

Dividing both sides by 2.

Solving for in terms of width.

Subtracting both sides.

∴

Substituting value of in terms of in equation A.

Using distribution.

Adding both sides.

subtracting both sides

We have a quadratic equation.

We solve for by factor method.

Splitting middle term into two terms such that the sum of the two = and product of two =

Factoring in pairs.

Factoring as a whole

So, we have

and

By adding 24 to one equation and adding 1 to other we get

and

and

So length can be found out by plugging value of in the length equation.

and

Since length is always the longer side of rectangle so,  the dimensions of rectangle can be given by.

length = 24 inches  (answer)

width = 1 inches (answer)

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)