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Algebra · perimeter of a square

P6 · Algebra · PSLE Maths

Question

Mei Ling designs a square sticker for a school event. Each side of the sticker is (m + 3) cm. (a) Express the perimeter of the sticker in terms of m. (b) When m = 5, what is the perimeter of the sticker in cm?

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Hint

A square has 4 equal sides. First write 4 × (m + 3), then simplify.

Show the answer and step-by-step explanation

Answer: Expression for the perimeter 4m+12 cm; Perimeter when m = 5 32 cm

  1. Draw the square — A square has 4 equal sides. Each side is m + 3 cm, so label all 4 sides m + 3.
  2. Perimeter is all sides — The perimeter is the distance all around the shape. Add the 4 equal sides: 4 lots of m + 3.
  3. Expand — Now multiply 4 into the brackets: 4 × m = 4m, and 4 × 3 = 12. So the perimeter is 4m + 12 cm.
  4. Substitute m = 5 — For the second part, m = 5. Replace m in the expression with 5.
  5. Write the answers — Therefore, the expression for the perimeter is 4m + 12 cm. When m = 5, the perimeter is 32 cm. 📌 Key idea: Perimeter of a square = 4 × side length. Simplify the algebraic expression first, then substitute the value.

Method: To find the perimeter of a square, use 4 × side length. With algebra, write and expand the expression first; when a value is given, substitute it for the letter and calculate.

Practice: 3 similar questions

  1. Siti draws a square bookmark. Each side is (n + 2) cm. (a) Express the perimeter of the bookmark in terms of n. (b) When n = 6, what is the perimeter in cm?
    Answer

    0 cm, 32 cm — Perimeter = 4 × (n + 2). Expand: 4 × n + 4 × 2 = 4n + 8. When n = 6, the perimeter = 4 × 6 + 8 = 24 + 8 = 32 cm.

  2. Raju makes a square coaster. Each side is (2p + 1) cm. (a) Express the perimeter of the coaster in terms of p. (b) When p = 4, what is the perimeter in cm?
    Answer

    0 cm, 36 cm — Perimeter = 4 × (2p + 1). Expand: 4 × 2p + 4 × 1 = 8p + 4. When p = 4, the perimeter = 8 × 4 + 4 = 32 + 4 = 36 cm.

  3. Ali uses ribbon around the outside of a square photo frame and leaves an extra 12 cm for tying a knot. Each outside side is (x + 5) cm. (a) Express the total length of ribbon needed in terms of x. (b) When x = 7, how many cm of ribbon is needed?
    Answer

    0 cm, 60 cm — Distance around the outside of the frame = 4 × (x + 5). Add the extra 12 cm, so total length = 4 × (x + 5) + 12. Expand: 4x + 20 + 12 = 4x + 32. When x = 7, the total length = 4 × 7 + 32 = 28 + 32 = 60 cm.

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