QuestionFind the perimeter equation for a rectangle with perimeter $120 \mathrm{~cm}$ and solve for $x$ . Options: a. $2x+5+6x-1=120$ , b. $4(6x-1)=120$ , c. $2(6x-1)+2(2x+5)=120$ , d. $(2x+5)(6x-1)=120$ .

Studdy Solution

STEP 1

Assumptions1. The perimeter of the rectangle is120 cm. The equations provided represent the perimeter of the rectangle3. We need to find the value of $x$ that makes the perimeter120 cm

STEP 2

We know that the perimeter of a rectangle is given by the formula $2(length + width)$ . We can use this to evaluate each equation.

STEP 3

Evaluate equation a.
$2x +5 +6x -1 =120$ Combine like terms.
$8x + =120$

STEP 4

Subtract4 from both sides of the equation.
$8x =120 -4$ $8x =116$

STEP 5

Divide both sides of the equation by8 to solve for $x$ .
$x = \frac{116}{8}$ $x =14.5$

STEP 6

Evaluate equation b.
$4(6x -1) =120$ Expand the equation.
$24x -4 =120$

STEP 7

Add4 to both sides of the equation.
$24x =120 +4$ $24x =124$

STEP 8

Divide both sides of the equation by24 to solve for $x$ .
$x = \frac{124}{24}$ $x =5.17$

STEP 9

Evaluate equation c.
$2(6x -) +2(2x +5) =120$ Expand the equation.
$12x -2 +4x + =120$ Combine like terms.
$16x +8 =120$

STEP 10

Subtract8 from both sides of the equation.
$16x =120 -8$ $16x =112$

STEP 11

Divide both sides of the equation by16 to solve for $x$ .
$x = \frac{112}{16}$ $x =7$

STEP 12

Evaluate equation d.
$(2x +5)(6x -) =120$ Expand the equation.
$12x^{2} -2x +30x -5 =120$ Combine like terms.
$12x^{2} +28x -5 =120$ This is a quadratic equation and cannot be solved for $x$ using simple algebra.

STEP 13

From the above steps, we see that only equation c gives a positive integer value for $x$ when the perimeter is120 cm. Therefore, the correct equation is c.
$2(6x -) +2(2x +5) =120$ And the solution for $x$ is7.

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QuestionFind the perimeter equation for a rectangle with perimeter $120 \mathrm{~cm}$ and solve for $x$ . Options: a. $2x+5+6x-1=120$ , b. $4(6x-1)=120$ , c. $2(6x-1)+2(2x+5)=120$ , d. $(2x+5)(6x-1)=120$ .

Studdy Solution

STEP 1

Assumptions1. The perimeter of the rectangle is120 cm. The equations provided represent the perimeter of the rectangle3. We need to find the value of $x$ that makes the perimeter120 cm

STEP 2

We know that the perimeter of a rectangle is given by the formula $2(length + width)$ . We can use this to evaluate each equation.

STEP 3

Evaluate equation a.
$2x +5 +6x -1 =120$ Combine like terms.
$8x + =120$

STEP 4

Subtract4 from both sides of the equation.
$8x =120 -4$ $8x =116$

STEP 5

Divide both sides of the equation by8 to solve for $x$ .
$x = \frac{116}{8}$ $x =14.5$

STEP 6

Evaluate equation b.
$4(6x -1) =120$ Expand the equation.
$24x -4 =120$

STEP 7

Add4 to both sides of the equation.
$24x =120 +4$ $24x =124$

STEP 8

Divide both sides of the equation by24 to solve for $x$ .
$x = \frac{124}{24}$ $x =5.17$

STEP 9

Evaluate equation c.
$2(6x -) +2(2x +5) =120$ Expand the equation.
$12x -2 +4x + =120$ Combine like terms.
$16x +8 =120$

STEP 10

Subtract8 from both sides of the equation.
$16x =120 -8$ $16x =112$

STEP 11

Divide both sides of the equation by16 to solve for $x$ .
$x = \frac{112}{16}$ $x =7$

STEP 12

Evaluate equation d.
$(2x +5)(6x -) =120$ Expand the equation.
$12x^{2} -2x +30x -5 =120$ Combine like terms.
$12x^{2} +28x -5 =120$ This is a quadratic equation and cannot be solved for $x$ using simple algebra.

STEP 13

From the above steps, we see that only equation c gives a positive integer value for $x$ when the perimeter is120 cm. Therefore, the correct equation is c.
$2(6x -) +2(2x +5) =120$ And the solution for $x$ is7.

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Studdy Solution

STEP 1

Assumptions1. The perimeter of the rectangle is120 cm. The equations provided represent the perimeter of the rectangle3. We need to find the value of xxx that makes the perimeter120 cm

STEP 2

We know that the perimeter of a rectangle is given by the formula 2(length+width)2(length + width)2(length+width). We can use this to evaluate each equation.

STEP 3

Evaluate equation a.2x+5+6x−1=1202x +5 +6x -1 =1202x+5+6x−1=120Combine like terms.8x+=1208x + =1208x+=120

STEP 4

Subtract4 from both sides of the equation.8x=120−48x =120 -48x=120−48x=1168x =1168x=116

STEP 5

Divide both sides of the equation by8 to solve for xxx.x=1168x = \frac{116}{8}x=8116​x=14.5x =14.5x=14.5

STEP 6

Evaluate equation b.4(6x−1)=1204(6x -1) =1204(6x−1)=120Expand the equation.24x−4=12024x -4 =12024x−4=120

STEP 7

Add4 to both sides of the equation.24x=120+424x =120 +424x=120+424x=12424x =12424x=124

STEP 8

Divide both sides of the equation by24 to solve for xxx.x=12424x = \frac{124}{24}x=24124​x=5.17x =5.17x=5.17

STEP 9

Evaluate equation c.2(6x−)+2(2x+5)=1202(6x -) +2(2x +5) =1202(6x−)+2(2x+5)=120Expand the equation.12x−2+4x+=12012x -2 +4x + =12012x−2+4x+=120Combine like terms.16x+8=12016x +8 =12016x+8=120

STEP 10

Subtract8 from both sides of the equation.16x=120−816x =120 -816x=120−816x=11216x =11216x=112

STEP 11

Divide both sides of the equation by16 to solve for xxx.x=11216x = \frac{112}{16}x=16112​x=7x =7x=7

STEP 12

STEP 13

From the above steps, we see that only equation c gives a positive integer value for xxx when the perimeter is120 cm. Therefore, the correct equation is c.2(6x−)+2(2x+5)=1202(6x -) +2(2x +5) =1202(6x−)+2(2x+5)=120And the solution for xxx is7.

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Assumptions1. The perimeter of the rectangle is120 cm. The equations provided represent the perimeter of the rectangle3. We need to find the value of $x$ that makes the perimeter120 cm

We know that the perimeter of a rectangle is given by the formula $2(length + width)$ . We can use this to evaluate each equation.

Evaluate equation a.
$2x +5 +6x -1 =120$ Combine like terms.
$8x + =120$

Subtract4 from both sides of the equation.
$8x =120 -4$ $8x =116$

Divide both sides of the equation by8 to solve for $x$ .
$x = \frac{116}{8}$ $x =14.5$

Evaluate equation b.
$4(6x -1) =120$ Expand the equation.
$24x -4 =120$

Add4 to both sides of the equation.
$24x =120 +4$ $24x =124$

Divide both sides of the equation by24 to solve for $x$ .
$x = \frac{124}{24}$ $x =5.17$

Evaluate equation c.
$2(6x -) +2(2x +5) =120$ Expand the equation.
$12x -2 +4x + =120$ Combine like terms.
$16x +8 =120$

Subtract8 from both sides of the equation.
$16x =120 -8$ $16x =112$

Divide both sides of the equation by16 to solve for $x$ .
$x = \frac{112}{16}$ $x =7$

From the above steps, we see that only equation c gives a positive integer value for $x$ when the perimeter is120 cm. Therefore, the correct equation is c.
$2(6x -) +2(2x +5) =120$ And the solution for $x$ is7.