Perimeter Algebra Question

Question

The perimeter of a rectangle can be represented by 2(2x+20) inches. The length of the rectangle can be represented by (2x+14), and its width can be represented by (4x-10). What are the length: and width: of this rectangle in inches?

Answer 1

We know the formula of perimeter of a Rectangle = 2 *( length + width )

Here from the problem Length = (2x+14),

Width = (4x-10),

Perimeter = 2(2x+20)

As per the formula substituting all the values in the formula,

2( 2x + 20 ) = 2 (2x +14 + 4x - 10)

to eliminate 2 , dividing both sides by 2 we get,

2x + 20 = 6x + 4

subtracting 2x from noth sides,

20 = 6x - 2x + 4

subtracting 4 both sides,

20- 4 = 4x

4x = 16

dividing both sides by 4

x = 4

plugging this value of x ,in the given condition ,

Length = ( 2*4 + 14 ) = 22 inches

Width + ( 4*4 - 10 ) = 6 inches

Perimeter = 2 ( 2*4 + 20 ) = 56 Inches

Answer 2

Hi

length = 22 inches

width = 6 inches

We need the formula for the Perimeter, P, of a rectangle and we are given the length and the width above

P = 2(length) + 2(width) = 2(2x + 20)

length = (2x + 14)

width = (4x - 10)

We can subsitute

P = 2(2x + 14) + 2(4x -10) = 2(2x + 20)

We have two equal representations of P

2(2x + 14) + 2(4x -10) = 2(2x + 20)

Divide both sides of the equations by 2

2x + 14 + 4x - 10 = 2x + 20

Move the variable to one side of equation and the constants to the other side

2x - 2x + 4x = 20 + 10 - 14

Combine like terms

4x = 16

Divide both sides of the equation by 4

x = 4

Plug x in the equations for the length and width

length = 2x + 14 = 2(4) + 14 = 22

width = 4x - 10 = 4(4) - 10 = 6

Next plug x in all the equation for the Perimeter and check it against the values above for the length and width

P = 2(2(4) + 20) = 2(22) + 2(6)

P = 2(8 + 20) = 44 + 12

P = 2(28) = 56

P = 56 = 56

I hope this helps if you have any questions just send me a message