Question

length / width of a rectangle
sheet 2
solve for x and then find the indicated measure.
1)
(3x - 10) in
2)
(2x - 29) yd
(-22 + 5x) in
(8 + x) yd
x=
width=
length=
3)
4)
(34 + 7x) ft
(-6x - 5) ft
(4x + 63) in
(9x + 28) in
x=
length=
x=
width=
5)
6)
(-8x) yd
(-2x + 30) yd
(-10x + 47) ft
(15 + 6x) ft
x=
width=
x=
length=

Explanation:

1)

Step1: Set up the equation

In a rectangle, opposite sides are equal. So \(3x - 10=-22 + 5x\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(-10=-22 + 2x\).
Add \(22\) to both sides: \(12 = 2x\).
Divide by \(2\): \(x = 6\).

Step3: Find the width

Substitute \(x = 6\) into \(3x-10\): \(3\times6 - 10=18 - 10 = 8\) in.

2)

Step1: Set up the equation

Since opposite sides of a rectangle are equal, \(2x-29=8 + x\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(x-29 = 8\).
Add \(29\) to both sides: \(x=37\).

Step3: Find the length

Substitute \(x = 37\) into \(2x - 29\): \(2\times37-29=74 - 29=45\) yd.

3)

Step1: Set up the equation

For the rectangle, \(34 + 7x=-6x - 5\).

Step2: Solve for \(x\)

Add \(6x\) to both sides: \(34+13x=-5\).
Subtract \(34\) from both sides: \(13x=-39\).
Divide by \(13\): \(x=-3\).

Step3: Find the length

Substitute \(x=-3\) into \(34 + 7x\): \(34+7\times(-3)=34 - 21 = 13\) ft.

4)

Step1: Set up the equation

Because opposite sides of a rectangle are equal, \(4x + 63=9x+28\).

Step2: Solve for \(x\)

Subtract \(4x\) from both sides: \(63 = 5x+28\).
Subtract \(28\) from both sides: \(35 = 5x\).
Divide by \(5\): \(x = 7\).

Step3: Find the width

Substitute \(x = 7\) into \(4x + 63\): \(4\times7+63=28 + 63=91\) in.

5)

Step1: Set up the equation

In the rectangle, \(-8x=-2x + 30\).

Step2: Solve for \(x\)

Add \(8x\) to both sides: \(0 = 6x+30\).
Subtract \(30\) from both sides: \(-30 = 6x\).
Divide by \(6\): \(x=-5\).

Step3: Find the width

Substitute \(x=-5\) into \(-8x\): \(-8\times(-5)=40\) yd.

6)

Step1: Set up the equation

Since opposite sides of a rectangle are equal, \(-10x + 47=15+6x\).

Step2: Solve for \(x\)

Add \(10x\) to both sides: \(47=15 + 16x\).
Subtract \(15\) from both sides: \(32 = 16x\).
Divide by \(16\): \(x = 2\).

Step3: Find the length

Substitute \(x = 2\) into \(-10x + 47\): \(-10\times2+47=-20 + 47=27\) ft.

Answer:

1. \(x = 6\), width \(=8\) in
2. \(x = 37\), length \(=45\) yd
3. \(x=-3\), length \(=13\) ft
4. \(x = 7\), width \(=91\) in
5. \(x=-5\), width \(=40\) yd
6. \(x = 2\), length \(=27\) ft