Equation Problems (Area)
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Question 1 of 5
1. Question
Find `x` if the area of the rectangle below is `165`cm².
- `x=` (7)
Hint
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Well Done!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Area of a Rectangle
`A=``L``times``W`First, label the values and form an equation using the Area of a Rectangle formula.
`L=(x+8)`cm`W=11`cm`A=165`cm²`A` `=` `L``times``W` `165` `=` `(x+8)``times``11` Substitute the values `165` `=` `11(x+8)` `11(x+8)` `=` `165` To solve for `x`, it needs to be alone on one side.Start by expanding the left side of the equation by using the Distributive Property.`11``(``x` `+8)` `=` `165` `11``x` `+``11``(8)` `=` `165` `11``x` `+88` `=` `165` Next, move `88` to the other side by subtracting `88` from both sides of the equation.`11``x` `+88` `=` `165` `11``x` `+88` `-88` `=` `165` `-88` `11``x` `=` `77` `88-88` cancels out Finally, remove `11` by dividing both sides of the equation by `11`.`11``x` `=` `77` `11``x``divide11` `=` `77``divide11` `x` `=` `7` `11divide11` cancels out `x=7` -
Question 2 of 5
2. Question
Find `y`.
- `y=` (4)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Area of a Rectangle
`A=``L``times``W`First, label the values and form an equation using the Area of a Rectangle formula.
`L=(6y-5)`cm`W=10`cm`A=190`cm²`A` `=` `L``times``W` `190` `=` `(6y-5)``times``10` Substitute the values `190` `=` `10(6y-5)` To solve for `y`, it needs to be alone on one side.Start by expanding the right side of the equation by using the Distributive Property.`190` `=` `10``(6``y` `-5)` `190` `=` `10``(6``y``)+``10``(-5)` `190` `=` `60``y` `-50` Next, move `50` to the other side by adding `50` to both sides of the equation.`190` `=` `60``y` `-50` `190` `+50` `=` `60``y` `-50` `+50` `240` `=` `60``y` `-50+50` cancels out Finally, remove `60` by dividing both sides of the equation by `60`.`240` `=` `60``y` `240``divide60` `=` `60``y``divide60` `4` `=` `y` `60divide60` cancels out `y` `=` `4` `y=4` -
Question 3 of 5
3. Question
Find `n` if the area of the triangle below is `140`cm².
- `n=` (13)
Hint
Help VideoCorrect
Good Job!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Area of a Triangle
`A=1/2``b``h`First, label the values and form an equation using the Area of a Triangle formula.
`b=(2n+9)`cm`h=8`cm`A=140`cm²`A` `=` `1/2``b``h` `140` `=` `1/2``(2n+9)``8` Substitute the values `140` `=` `4(2n+9)` Simplify `4(2n+9)` `=` `140` To solve for `n`, it needs to be alone on one side.Start with removing `4` by dividing both sides of the equation by `4`.`4(2``n` `+9)` `=` `140` `4(2``n` `+9)``divide4` `=` `140``divide4` `2``n` `+9` `=` `35` `4-:4` cancels out Next, move `9` to the other side by subtracting `9` from both sides of the equation.`2``n` `+9` `=` `35` `2``n` `+9` `-9` `=` `35` `-9` `2``n` `=` `26` `9-9` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`2``n` `=` `26` `2``n``divide2` `=` `26``divide2` `n` `=` `13` `2divide2` cancels out `n=13` -
Question 4 of 5
4. Question
Find `h`.
- `h=` (20)cm
Hint
Help VideoCorrect
Excellent!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Area of a Triangle
`A=1/2``b``h`First, label the values and form an equation using the Area of a Triangle formula.
`A=170`cm²`b=17`cm`h=?`cm`A` `=` `1/2``b``h` `170` `=` `1/2``(17)``h` Substitute the values To solve for `h`, it needs to be alone on one side.Start with removing `1/2` by multiplying both sides of the equation by `2`.`170` `=` `1/2 (17)``h` `170``times2` `=` `1/2 (17)``h``times2` `340` `=` `17``h` `1/2times2` cancels out Finally, remove `17` by dividing both sides of the equation by `17`.`340` `=` `17``h` `340``divide17` `=` `17``h``divide17` `20` `=` `h` `17divide17` cancels out `h` `=` `20`cm `h=20`cm -
Question 5 of 5
5. Question
Find the dimensions and the area of the rectangle below.
-
`L=` (69)cm`W=` (7)cm`A=` (483)cm²
Hint
Help VideoCorrect
Exceptional!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Area of a Rectangle
`A=``L``times``W`First, find the value of `x`.Do this by forming an equation knowing that opposite sides of a rectangle are equal.
`3x+6` `=` `4x-15` To solve for `x`, it needs to be alone on one side.Start by moving `3x` to the other side by subtracting `3x` from both sides of the equation.`3``x` `+6` `=` `4``x` `-15` `3``x` `+6` `-3x` `=` `4``x` `-15` `-3x` `6` `=` `x` `-15` `3x-3x` cancels out Next, move `15` to the other side by adding `15` to both sides of the equation.`6` `=` `x` `-15` `6` `+15` `=` `x` `-15` `+15` `21` `=` `x` `-15+15` cancels out `x` `=` `21` Substitute `x=21` to find the dimensions of the rectangle.Width `=` `1/3``x` `=` `1/3``(21)`cm `=` `7`cm Length `=` `3``x` `+6` `=` `3``(21)` `+6` `=` `63+6` `=` `69`cm Finally, use the dimensions of the rectangle to find its Area.
`L=69` cm`W=7`cm`A` `=` `L``times``W` Area Formula `=` `69``times``7` Substitute the values `=` `483`cm² Simplify `L=69`cm`W=7`cm`A=483`cm² -
Quizzes
- One Step Equations – Add and Subtract 1
- One Step Equations – Add and Subtract 2
- One Step Equations – Add and Subtract 3
- One Step Equations – Add and Subtract 4
- One Step Equations – Multiply and Divide 1
- One Step Equations – Multiply and Divide 2
- One Step Equations – Multiply and Divide 3
- One Step Equations – Multiply and Divide 4
- Two Step Equations 1
- Two Step Equations 2
- Two Step Equations 3
- Two Step Equations 4
- Multi-Step Equations 1
- Multi-Step Equations 2
- Solve Equations using the Distributive Property 1
- Solve Equations using the Distributive Property 2
- Solve Equations using the Distributive Property 3
- Equations with Variables on Both Sides 1
- Equations with Variables on Both Sides 2
- Equations with Variables on Both Sides 3
- Equations with Variables on Both Sides (Fractions) 1
- Equations with Variables on Both Sides (Fractions) 2
- Solve Equations with Variables on Both Sides using the Distributive Property 1
- Solve Equations with Variables on Both Sides using the Distributive Property 2
- Solve Equations with Variables on Both Sides using the Distributive Property 3
- Solve Equations with Variables on Both Sides using the Distributive Property 4
- Equation Word Problems 1
- Equation Word Problems 2
- Equation Word Problems 3
- Equation Word Problems 4
- Equation Word Problems (Age)
- Equation Word Problems (Money)
- Equation Word Problems (Harder)
- Equation Problems with Substitution
- Equation Problems (Geometry) 1
- Equation Problems (Geometry) 2
- Equation Problems (Perimeter)
- Equation Problems (Area)
- Change the Subject of an Equation 1
- Change the Subject of an Equation 2
- Change the Subject of an Equation 3