The dimensions of the tickets are 20 cm and 9 cm
Step-by-step explanation:
Let us revise the formulas of area and perimeter of a rectangle
- Area of a rectangle = l × w, where l is the length and w is the width
- Perimeter of a rectangle = 2l + 2w
∵ The area of an airplane ticket is 180 cm²
∵ The area of a rectangle = l × w
∴ l × w = 180
∴ l w = 180 ⇒ (1)
∵ The perimeter of it is 58 cm
∵ The perimeter of a rectangle = 2l + 2w
∴ 2l + 2w = 58
- Divide both sides by 2
∴ l + w = 29 ⇒ (2)
Now we have system of equations to solve it
Use equation (2) to find w in terms of l
∵ l + w = 29
- Subtract l from both sides
∴ w = 29 - l ⇒ (3)
- Substitute equation (3) in equation (1)
∵ l(29 - l) = 180
∴ 29l - l² = 180
- Subtract 180 from both sides
∴ 29l - l² - 180 = 0
- Multiply both sides by -1 and re-arrange the terms from
greatest power of l
∴ l² - 29l + 180 = 0
Let us factorize it into two factors to find the value of l
∵ l² = l × l
∵ 180 = 20 × 9
∵ 20 × l + 9 × l = 20l + 9l = 29l
∴ l² - 29l + 180 = (l - 20)(l - 9)
- Equate them by 0 to find l
∴ (l - 20)(l - 9) = 0
- Equate each factor by 0
∵ l - 20 = 0
- Add 20 to both sides
∴ l = 20
- Substitute the value of l in equation (3) to find w
∵ w = 29 - 20
∴ w = 9
OR
∵ l - 9 = 0
- Add 9 to both sides
∴ l = 9
- Substitute the value of l in equation (3) to find w
∵ w = 29 - 9
∴ w = 20
The dimensions of the tickets are 20 cm and 9 cm
Learn more:
You can learn more about the system of equations in brainly.com/question/3739260
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