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A rhombus is a rectangle with opposite sides equal. Its diagonals are perpendicular bisectors of each other. It has rotational symmetry of order 2. Its diagonals bisect the angles. Find the area of the rhombus with diagonals 10 cm and 12 cm.

Mathematics

ScanSolve AI Answer

Answer

8 cm\text{8 cm}

Step-by-step solution

4 steps

  1. Identify the given information and the relevant theorem.

    The problem describes a triangle PQR where S is the midpoint of PQ and T is the midpoint of PR. The length of ST is given as 4 cm4 \text{ cm}. We need to find the length of QR. This scenario directly applies the Midpoint Theorem.

  2. State the Midpoint Theorem.

    The Midpoint Theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side.

  3. Apply the theorem to find QR.

    According to the Midpoint Theorem, since S and T are midpoints of PQ and PR respectively, the length of ST is half the length of QR.

    ST=12QRST = \frac{1}{2} QR

  4. Substitute the given value and solve for QR.

    We are given ST=4 cmST = 4 \text{ cm}.

    4=12QR4 = \frac{1}{2} QR

    To find QR, multiply both sides by 2:

    QR=4×2QR = 4 \times 2 QR=8 cmQR = 8 \text{ cm}

    The length of QR is:

    8 cm\text{8 cm}
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