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Question 1 of 3
1. Question
Find `x` if the perimeter of the triangle below is `44`cm.
`x=`(8)
Correct
Fantastic!
Incorrect
Help Video
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
First, form an equation knowing that the Perimeter of a shape is the sum of all sides.
`P=44`cm
Side `1=x` cm
Side `2=(x+6)`cm
Side `3=(3x-2)`cm
`P`
`=`
Side `1` `+`Side `2` `+`Side `3`
`44`
`=`
`x` `+``(x+6)` `+``(3x-2)`
Substitute the values
`44`
`=`
`5x+4`
Simplify
`5x+4`
`=`
`44`
To solve for `x`, it needs to be alone on one side.
Start by moving `4` to the other side by subtracting `4` from both sides of the equation.
`5``x` `+4`
`=`
`44`
`5``x` `+4` `-4`
`=`
`44` `-4`
`5``x`
`=`
`40`
`4-4` cancels out
Finally, remove `5` by dividing both sides of the equation by `5`.
`5``x`
`=`
`40`
`5``x``divide5`
`=`
`40``divide5`
`x`
`=`
`8`
`5divide5` cancels out
`x=8`
Hint
Help Video
Question 2 of 3
2. Question
An isosceles triangle has a perimeter of `55`cm and a base that is `5`cm less than either of the other `2` equal sides. What are the lengths of all three sides?
Equal Side `1=`(20)cm
Equal Side `2=`(20)cm
Base `=`(15)cm
Correct
Good Job!
Incorrect
Help Video
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
First, label the values and form an equation knowing that the Perimeter of a shape is the sum of all sides.
Equal Side `1=x`
Equal Side `2=x`
Base `=(x-5)`
`P=55`cm
Equal Side `1` `+`Equal Side `2` `+`Base
`=`
`P`
`x` `+``x` `+``x-5`
`=`
`55`
Substitute the values
`3x-5`
`=`
`55`
Simplify
To solve for `x`, it needs to be alone on one side.
Start by moving `5` to the other side by adding `5` to both sides of the equation.
`3``x` `-5`
`=`
`55`
`3``x` `-5` `+5`
`=`
`55` `+5`
`3``x`
`=`
`60`
`-5+5` cancels out
Finally, remove `3` by dividing both sides of the equation by `3`.
`3``x`
`=`
`60`
`3``x``divide3`
`=`
`60``divide3`
`x`
`=`
`20`
`3divide3` cancels out
Substitute `x=20` to find each side length.
Equal Side `1`
`=`
`x`
`=`
`20`cm
Equal Side `2`
`=`
`x`
`=`
`20`cm
Base
`=`
`x` `-5`
`=`
`20` `-5`
`=`
`15`cm
Check our work
To confirm our answer, add the `3` numbers and check if the sum is `55`.
`20+20+15`
`=`
`55`
`55`
`=`
`55`
Since the equation is true, the answer is correct.
Equal Side `1=20`cm
Equal Side `2=20`cm
Base `=15`cm
Hint
Help Video
Question 3 of 3
3. Question
A rectangle is twice as long as it is wide. The total perimeter is `126`cm. What are the dimensions of this rectangle?
Length`=`(42)cm
Width`=`(21) cm
Correct
Excellent!
Incorrect
Help Video
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.
First, draw a rectangle and label it using the given statement: “A rectangle is twice as long as it is wide.”
This means if the width is `w`, the length should be `2w`
Form an equation knowing that the Perimeter of a shape is the sum of all sides.
`P=126`cm
Side `1` and `2=w` cm
Side `3` and `4=2w` cm
`P`
`=`
Side `1` `+`Side `2` `+`Side `3` `+`Side `4`
`126`
`=`
`w` `+``w` `+``2w` `+``2w`
Substitute the values
`126`
`=`
`6w`
Simplify
`6w`
`=`
`126`
Now, to solve for `w`, it needs to be alone on one side.
Remove `6` by dividing both sides of the equation by `6`.
`6``w`
`=`
`126`
`6``w``divide6`
`=`
`126` `divide6`
`w`
`=`
`21`
`6divide6` cancels out
Finally, substitute `w=21` to the dimensions of the rectangle.
