课爱 classai 中文

Topics › Algebra › Q143

Algebra · perimeter and area of a rectangle

P6 · Algebra · PSLE Maths

Question

For the school open house, Siti makes a rectangular notice board. Its length is (3y + 8) cm and its breadth is (y + 4) cm. (a) Express its perimeter in terms of y. (b) Express its area in terms of y and simplify it. (c) Find the perimeter and area when y = 6.

Try it yourself · watch the animation →

Hint

A rectangle has two lengths and two breadths. First write perimeter = length + breadth + length + breadth, and area = length × breadth, then expand and simplify.

Show the answer and step-by-step explanation

Answer: Perimeter expression 8y+24 cm; Area expression 3y^2+20y+32 cm²; Perimeter when y = 6 72 cm; Area when y = 6 260 cm²

  1. Label 4 sides — Draw the rectangle first. Opposite sides of a rectangle are equal, so both lengths are (3y + 8) cm and both breadths are (y + 4) cm.
  2. Perimeter is 4 sides — The perimeter is the distance around the rectangle: length + breadth + length + breadth. Use a bar model to arrange the four sides in a line.
  3. Simplify perimeter — Group the two lengths and two breadths: 2 lots of (3y + 8) and 2 lots of (y + 4).
  4. Write area — Area is the space covered inside the shape, so use length × breadth. Write the product first, then expand and collect like terms.
  5. Substitute y = 6 — Now substitute y = 6. Length = 3 × 6 + 8 = 26 cm, and breadth = 6 + 4 = 10 cm.
  6. Evaluate — Perimeter = 8 × 6 + 24 = 72 cm. Area = 26 × 10 = 260 cm². 📌 Key idea: write the formula with the letter first, then substitute the value; perimeter is around the outside, area covers the inside.

Method: Label all four sides first. Add the four sides and simplify for the perimeter; multiply length by breadth, then expand and collect like terms for the area. Then substitute the value of y.

Practice: 3 similar questions

  1. Mei Ling makes a rectangular bookmark. Its length is (2y + 5) cm and its breadth is (y + 3) cm. (a) Express its perimeter and area in terms of y and simplify them. (b) Find the perimeter and area when y = 7.
    Answer

    0 cm, 0 cm², 58 cm, 190 cm² — Perimeter P = 2(2y + 5) + 2(y + 3) = 4y + 10 + 2y + 6 = 6y + 16. Area A = (2y + 5)(y + 3) = 2y² + 6y + 5y + 15 = 2y² + 11y + 15. When y = 7, length = 2 × 7 + 5 = 19 cm and breadth = 7 + 3 = 10 cm. Perimeter = 6 × 7 + 16 = 58 cm; area = 19 × 10 = 190 cm².

  2. Raju's class has a rectangular vegetable garden. Its length is (4y - 3) m and its breadth is (2y + 1) m. (a) Express its perimeter and area in terms of y and simplify them. (b) Find the perimeter and area when y = 5.
    Answer

    0 m, 0 m², 56 m, 187 m² — Perimeter P = 2(4y - 3) + 2(2y + 1) = 8y - 6 + 4y + 2 = 12y - 4. Area A = (4y - 3)(2y + 1) = 8y² + 4y - 6y - 3 = 8y² - 2y - 3. When y = 5, length = 4 × 5 - 3 = 17 m and breadth = 2 × 5 + 1 = 11 m. Perimeter = 12 × 5 - 4 = 56 m; area = 17 × 11 = 187 m².

  3. Ali designs a small rectangular playground. Its length is (5y + 2) m and its breadth is (2y + 7) m. (a) Express its perimeter and area in terms of y and simplify them. (b) Find the perimeter and area when y = 9.
    Answer

    0 m, 0 m², 144 m, 1175 m² — Perimeter P = 2(5y + 2) + 2(2y + 7) = 10y + 4 + 4y + 14 = 14y + 18. Area A = (5y + 2)(2y + 7) = 10y² + 35y + 4y + 14 = 10y² + 39y + 14. When y = 9, length = 5 × 9 + 2 = 47 m and breadth = 2 × 9 + 7 = 25 m. Perimeter = 14 × 9 + 18 = 144 m; area = 47 × 25 = 1175 m².

Learn it on classai

An animation walks through each step, then 3 similar questions check it stuck; mistakes come back for review after 1, 3 and 7 days.

Open this question →

More Algebra questions

Algebra · simplify and substituteAt a school carnival, Siti bought n game coupons. Ali bought 2 more coupons than Siti. Ra…Algebra · form and evaluate expressionsMei Ling bought 4 meal coupons at $n each and 3 drink coupons at $2 each for a school car…Algebra · combining like termsRaju had 6a + 15 football cards. He gave 2a football cards to Siti and then bought 9 more…Pattern · matchsticksAli uses matchsticks to make a row of equal squares. Figure 1 has 1 square. Figure 2 has …Algebra · age expressionsRaju is x years old now. His sister, Siti, is 4 years younger than him. What is the sum o…Algebra · expressing quantitiesSiti bought 3 boxes of pens. Each box had k pens. She gave 5 pens to her classmates. (a) …