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📝 Perimeter of rectangle formula (P = 2L + 2W) (11 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 11 questions available

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What is Perimeter of rectangle formula (P = 2L + 2W)?

Definition:
The perimeter of a rectangle is the total distance around the outside of the rectangle, calculated by adding twice the length and twice the width, expressed as $P = 2L + 2W$ , where $L$ is the length and $W$ is the width, and this formula applies to any rectangle, representing the sum of all four sides, with opposite sides being equal.

Working:
To find the perimeter, measure or know the length and width in the same units, then multiply each by 2 and add the products, so $P = 2(L + W)$ , and if you know the perimeter and one dimension, you can solve for the other by rearranging the formula, e.g., $L = \frac{P - 2W}{2}$ , and the result is in linear units like meters or feet.

Example:
A rectangular garden has a length of 15 meters and a width of 10 meters; its perimeter is $P = 2(15) + 2(10) = 30 + 20 = 50$ meters, meaning you would need 50 meters of fencing to enclose the garden.

Reason:
The perimeter formula is crucial for practical tasks like fencing yards, framing walls, or building borders, as it helps determine the required materials and costs, and it is a fundamental concept in geometry and real-life construction.

Easy

Medium

Hard

📝 All Perimeter of rectangle formula (P = 2L + 2W) MCQs

Q1. A rectangle has length $12$ cm and width $7$ cm. Which expression correctly represents its perimeter?

12+7

2(12+7)

✅

12\times7

2(12-7)

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: A rectangle has two equal lengths and two equal widths. Therefore, adding all four sides gives $12+7+12+7=38$ , which is equivalently written as $2(12+7)$ .

Q2. A rectangle has perimeter $50$ m and length $15$ m. What is its width?

5

10

m ✅

15

20

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Using $P=2L+2W$ , substitute $50=2(15)+2W$ . This gives $50=30+2W$ , so $20=2W$ , and therefore $W=10$ meters.

Q3. Two rectangles have the same perimeter of $48$ cm. Rectangle A is $14$ cm by $10$ cm, while Rectangle B is $16$ cm by $8$ cm. What conclusion is correct?

A.A has greater perimeter

B.B has greater perimeter

C.Both have equal perimeter ✅

D.Their areas must also be equal

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Rectangle A has perimeter $2(14+10)=48$ cm, while Rectangle B has perimeter $2(16+8)=48$ cm. Equal perimeters do not require equal dimensions or equal areas.

Q4. A student claims that increasing a rectangle's length by $3$ cm increases its perimeter by only $3$ cm. Which reasoning best evaluates the claim?

A.Correct, because only length changes

B.Incorrect, because both opposite lengths increase by

3

cm ✅

C.Correct, because width determines perimeter

D.Incorrect, because the area must also increase

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: A rectangle has two sides with the length measurement. Increasing the length by $3$ cm increases both corresponding sides, so the total perimeter increases by $6$ cm.

Q5. A garden is $18$ m long and $11$ m wide. A farmer wants fencing around the entire boundary but leaves a $2$ -m opening for a gate. How much fencing is required?

A.58 m

B.56 m ✅

C.54 m

D.52 m

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The complete perimeter is $2(18)+2(11)=58$ m. Since the gate creates a $2$ -m unfenced opening, subtracting $2$ gives $56$ meters of fencing.

Q6. A rectangular poster has perimeter $74$ cm. Its length is $9$ cm greater than its width. Which dimensions satisfy these conditions?

23

cm by

14

cm ✅

22

cm by

15

20

cm by

17

24

cm by

13

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: Let the width be $W$ , so the length is $W+9$ . Then $74=2(W+9)+2W$ , giving $74=4W+18$ , so $W=14$ and $L=23$ .

Q7. A school wants to place decorative tape around a rectangular display measuring $2.4$ m by $1.7$ m. Tape is sold only in whole-meter rolls. What is the minimum number of meters of tape the school should buy?

A.6 m

B.7 m ✅

C.8 m

D.9 m

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The display perimeter is $2(2.4)+2(1.7)=8.2$ m. Because the tape must be purchased in whole-meter rolls, the school needs to round upward and buy $9$ meters.

Q8. A rectangular playground has perimeter $120$ m. A student says its dimensions must be $30$ m by $30$ m because half of $120$ is $60$ . What is wrong with this reasoning?

A.The dimensions must multiply to

120

B.The perimeter gives

L+W=60

, not necessarily

L=W=30

✅

C.The perimeter should be divided by

4

only

D.A rectangle cannot have equal sides

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: From $120=2L+2W$ , dividing by $2$ gives $L+W=60$ . Many dimension pairs satisfy this, such as $35$ and $25$ , so equal dimensions are not required.

Q9. A rectangular field has length $25$ m and width $14$ m. A contractor measures the boundary as $25+14=39$ m. What should the contractor report instead?

A.39 m

B.50 m

C.78 m ✅

D.350 m

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The measurement $25+14$ accounts for only one length and one width. Since both measurements occur twice around the rectangle, the correct perimeter is $2(25)+2(14)=78$ meters.

Q10. A graph shows the relationship between rectangle length $L$ and perimeter $P$ for a fixed width of $6$ cm. Which equation should describe the graph?

P=2L+6

P=L+12

P=2L+12

✅

P=6L+2

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: With width fixed at $6$ cm, the perimeter becomes $P=2L+2(6)$ , or $P=2L+12$ . Therefore, the graph should have slope $2$ and vertical intercept $12$ .

Q11. A student calculates the perimeter of a $16$ -cm by $9$ -cm rectangle as $2(16\times9)=288$ cm. Which correction best explains the error?

A.The student should add the dimensions before multiplying by

2

✅

B.The student should subtract the dimensions

C.The student should divide the product by

2

D.The student's answer is correct

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Multiplying length and width calculates area, not perimeter. For perimeter, the four side lengths are added, giving $2L+2W=2(16)+2(9)=50$ cm.

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