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To complete Table 13.1 for rectangles, we use the formula for the perimeter of a rectangle: P = 2 x (l + b), where l is the length and b is the breadth. We will also use rearranged forms to

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To complete Table 13.1 for rectangles, we use the formula for the perimeter of a rectangle: P=2×(l+b)P = 2 \times (l + b), where ll is the length and bb is the breadth. We will also use rearranged forms to find length or breadth: l=P2−bl = \frac{P}{2} - b and b=P2−lb = \frac{P}{2} - l.

  • Assumption for inconsistent units: For rows e, j, and n, where length and breadth or perimeter are given in different units (e.g., cm and m), we will assume consistency by converting the smaller unit to match the larger unit's context or by assuming a typo in the unit. Specifically:
    • For row e, we assume breadth is 212 cm2\frac{1}{2} \text{ cm} instead of 212 m2\frac{1}{2} \text{ m}.
    • For row j, we assume breadth is 0.9 m0.9 \text{ m} instead of 0.9 cm0.9 \text{ cm}.
    • For row n, we assume breadth is 7.5 m7.5 \text{ m} instead of 7.5 cm7.5 \text{ cm} to match the perimeter's unit.

  1. Calculate the perimeter for rows where length and breadth are given.

    • a) l=3 cml = 3 \text{ cm}, b=2 cmb = 2 \text{ cm} P=2×(3 cm+2 cm)=2×5 cm=10 cmP = 2 \times (3 \text{ cm} + 2 \text{ cm}) = 2 \times 5 \text{ cm} = 10 \text{ cm}
    • b) l=5 ml = 5 \text{ m}, b=4 mb = 4 \text{ m} P=2×(5 m+4 m)=2×9 m=18 mP = 2 \times (5 \text{ m} + 4 \text{ m}) = 2 \times 9 \text{ m} = 18 \text{ m}
    • c) l=16 cml = 16 \text{ cm}, b=10 cmb = 10 \text{ cm} P=2×(16 cm+10 cm)=2×26 cm=52 cmP = 2 \times (16 \text{ cm} + 10 \text{ cm}) = 2 \times 26 \text{ cm} = 52 \text{ cm}
    • d) l=212 m=52 ml = 2\frac{1}{2} \text{ m} = \frac{5}{2} \text{ m}, b=1 mb = 1 \text{ m} P=2×(52 m+1 m)=2×(52 m+22 m)=2×72 m=7 mP = 2 \times \left(\frac{5}{2} \text{ m} + 1 \text{ m}\right) = 2 \times \left(\frac{5}{2} \text{ m} + \frac{2}{2} \text{ m}\right) = 2 \times \frac{7}{2} \text{ m} = 7 \text{ m}
    • e) l=6 cml = 6 \text{ cm}, b=212 cm=2.5 cmb = 2\frac{1}{2} \text{ cm} = 2.5 \text{ cm} (assuming breadth is in cm) P=2×(6 cm+2.5 cm)=2×8.5 cm=17 cmP = 2 \times (6 \text{ cm} + 2.5 \text{ cm}) = 2 \times 8.5 \text{ cm} = 17 \text{ cm}
    • f) l=812 m=172 ml = 8\frac{1}{2} \text{ m} = \frac{17}{2} \text{ m}, b=412 m=92 mb = 4\frac{1}{2} \text{ m} = \frac{9}{2} \text{ m} P=2×(172 m+92 m)=2×262 m=2×13 m=26 mP = 2 \times \left(\frac{17}{2} \text{ m} + \frac{9}{2} \text{ m}\right) = 2 \times \frac{26}{2} \text{ m} = 2 \times 13 \text{ m} = 26 \text{ m}
    • i) l=7.35 cml = 7.35 \text{ cm}, b=7.15 cmb = 7.15 \text{ cm} P=2×(7.35 cm+7.15 cm)=2×14.50 cm=29 cmP = 2 \times (7.35 \text{ cm} + 7.15 \text{ cm}) = 2 \times 14.50 \text{ cm} = 29 \text{ cm}
    • j) l=9 ml = 9 \text{ m}, b=0.9 mb = 0.9 \text{ m} (assuming breadth is in m) P=2×(9 m+0.9 m)=2×9.9 m=19.8 mP = 2 \times (9 \text{ m} + 0.9 \text{ m}) = 2 \times 9.9 \text{ m} = 19.8 \text{ m}

  2. Calculate the length for rows where breadth and perimeter are given.

    • g) b=3.2 cmb = 3.2 \text{ cm}, P=16.6 cmP = 16.6 \text{ cm} l=16.6 cm2−3.2 cm=8.3 cm−3.2 cm=5.1 cml = \frac{16.6 \text{ cm}}{2} - 3.2 \text{ cm} = 8.3 \text{ cm} - 3.2 \text{ cm} = 5.1 \text{ cm}
    • k) b=8 mb = 8 \text{ m}, P=36 mP = 36 \text{ m} l=36 m2−8 m=18 m−8 m=10 ml = \frac{36 \text{ m}}{2} - 8 \text{ m} = 18 \text{ m} - 8 \text{ m} = 10 \text{ m}
    • n) b=7.5 mb = 7.5 \text{ m} (assuming breadth is in m), P=45 mP = 45 \text{ m} l=45 m2−7.5 m=22.5 m−7.5 m=15 ml = \frac{45 \text{ m}}{2} - 7.5 \text{ m} = 22.5 \text{ m} - 7.5 \text{ m} = 15 \text{ m}
    • o) b=6 mb = 6 \text{ m}, P=33 mP = 33 \text{ m} l=33 m2−6 m=16.5 m−6 m=10.5 ml = \frac{33 \text{ m}}{2} - 6 \text{ m} = 16.5 \text{ m} - 6 \text{ m} = 10.5 \text{ m}

  3. Calculate the breadth for rows where length and perimeter are given.

    • h) l=4.3 cml = 4.3 \text{ cm}, P=10.2 cmP = 10.2 \text{ cm}
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