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The problem states that the area of the second triangle (A2) is double the area of the first triangle (A1).

Mathematics

ScanSolve AI Answer

Answer

C

Step-by-step solution

4 steps

  1. Identify the given information for the first triangle.

    The base of the first triangle is b1=14b_1 = 14 cm.
    The area of the first triangle is A1=98 cm2A_1 = 98 \text{ cm}^2.

  2. Calculate the area of the second triangle.

    The problem states that the area of the second triangle (A2A_2) is double the area of the first triangle (A1A_1).

    A2=2×A1A_2 = 2 \times A_1 A2=2×98 cm2A_2 = 2 \times 98 \text{ cm}^2 A2=196 cm2A_2 = 196 \text{ cm}^2

  3. Identify the given information for the second triangle.

    The base of the second triangle is b2=14b_2 = 14 cm (same as the first triangle).
    The area of the second triangle is A2=196 cm2A_2 = 196 \text{ cm}^2.
    We need to find the height of the second triangle, h2h_2.

  4. Use the formula for the area of a triangle to find the height of the second triangle.

    The formula for the area of a triangle is:

    A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}

    For the second triangle:

    A2=12×b2×h2A_2 = \frac{1}{2} \times b_2 \times h_2

    Substitute the known values:

    196 cm2=12×14 cm×h2196 \text{ cm}^2 = \frac{1}{2} \times 14 \text{ cm} \times h_2 196 cm2=7 cm×h2196 \text{ cm}^2 = 7 \text{ cm} \times h_2

    Now, solve for h2h_2:

    h2=196 cm27 cmh_2 = \frac{196 \text{ cm}^2}{7 \text{ cm}} h2=28 cmh_2 = 28 \text{ cm}

    The height of the second triangle is 28 cm.
    Comparing this with the given options:
    A. 21 cm
    B. 7 cm
    C. 28 cm
    D. 14 cm

    The correct option is C.

    The final answer is 28 cm\boxed{\text{28 cm}}.

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