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Identify the rhombus among the given shapes and calculate the perimeter of a triangle with two sides given.

Mathematics

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Answer

10 cm\text{10 cm}

Step-by-step solution

5 steps
  1. Identify the definition of a rhombus.

    A rhombus is a quadrilateral (a four-sided polygon) in which all four sides are of equal length. It is also a type of parallelogram, meaning its opposite sides are parallel.

  2. Examine the given shapes.

    • The first shape is a hexagon (six sides).
    • The second shape is a circle.
    • The third shape is a triangle (three sides).
    • The fourth shape is a quadrilateral with opposite sides marked as parallel (indicated by the arrows). This shape is a parallelogram. Among the given options, this is the only quadrilateral, and a rhombus is a special type of parallelogram. Therefore, this shape represents a rhombus.

    The shape that is a rhombus is the parallelogram (the fourth shape).


  3. Write the formula for the perimeter of a triangle.

    The perimeter (PP) of a triangle is the sum of the lengths of its three sides (s1,s2,s3s_1, s_2, s_3).

    P=s1+s2+s3P = s_1 + s_2 + s_3
  4. Substitute the given values into the formula.

    The perimeter is 25 cm25 \text{ cm}. The lengths of two sides are 7 cm7 \text{ cm} and 8 cm8 \text{ cm}. The third side is BB.

    25 cm=7 cm+8 cm+B25 \text{ cm} = 7 \text{ cm} + 8 \text{ cm} + B
  5. Solve for BB.

    First, add the known side lengths:

    25 cm=(7+8) cm+B25 \text{ cm} = (7 + 8) \text{ cm} + B 25 cm=15 cm+B25 \text{ cm} = 15 \text{ cm} + B

    Now, subtract 15 cm15 \text{ cm} from both sides to find BB:

    B=25 cm−15 cmB = 25 \text{ cm} - 15 \text{ cm} B=10 cmB = 10 \text{ cm}

    The length of B is 10 cm\text{10 cm}.

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