posted by .

The sides AB and AC of triangle ABC have lengths of 4 inches and 7 inches, respectively. The median AM is 3.5 inches. What is the EXACT length of BC. Show your work.

  • Geometry -

    extend AM its own length of 3.5 to point D.
    Join BD and CD
    You now have a quadrilateral where the diagonals AD and BC bisect each other.
    So ABDC must be a parallelogram .
    In triangle ADC you could now use the cosine law to find angle DAC

    Once you have that you can use the cosine law again to find MC in triangle AMC
    double MC to find BC

  • Geometry -

    Triangle ABC, A at the top, B & C at the bottom, B left & C right.

    The length of a triangle median is defined by
    (Ma)^2 = (b^2 + c^2)/2 - a^2/4. (Ma is the median from vertex A to side "a".)
    (Mb)^2 = (a^2 + c^2)/2 - b^2/4
    (Mc)^2 = (a^2 + b^2)/2 - c^2/4

    Letting BC = a, AB = c = 4, AC = b = 7 and AH = 3.5

    Then, (3.5^2) = (7^2 + 4^2)/2 - a^2/4

    Multiplying through by 4 yields 4(3.5)^2 = 2(49 + 16) - a^2 or

    49 = 130 - a^2 or a^2 = 130 - 49 = 81 making a = 9 = BC.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    The sum of the lengths of the sides of triangle ABC is 25 in. The lengths of sides AB and BC are 9 inches and 8 inches. Find the length of side AC and classify the triangle.
  2. Math

    The sum of the lengths of the sides of triangle ABC is 38in. The length of sides AB and BC are 14 inches and 11 inches. Find the length of side AC and classify the triangle.
  3. Algebra 2

    Can you double check my answer The lengths of the sides of a rectangular window have the ratio 1.6 to 1. The area of the window is 2,560 square inches. What are the dimensions of the window?
  4. Math

    1) what is the length of the diagonal of a square whose sides are 3 inches long. A. 9 inches B. 3 square root 2 inches**** C. 6 inches D. 18 inches 2) which set of measure could be the side lengths of a right triangle?
  5. Geometry

    The lengths of the sides of a triangle are 3,5, and 7 inches. How many inches long is the shortest side of a similar triangle that has a perimeter of 75 inches?
  6. geometry

    Triangle ABC and triangle XYZ are similar. If AB, BC, and AC are 7 inches, 9 inches, and 10 inches respectively, and XY is 9 inches, find XZ to the nearest tenth of an inch.
  7. math

    The hypotenuse of a triangle is 13 inches long. Which of the follwoing pairsof measurements could be correct for the lengths of the other two sides of triangle: a:2.5 and 4 inches, b:2.5 and 6 inches,c:5 and 8 inches,d:5 and 12 inches
  8. geometry

    if the lengths of the sides of one triangle are 2 inches 5 inches and 7 inches respectively in the shortest leg of a similar triangle is 4 inches what is the perimeter of the second triangle in inches?
  9. Geometry

    1.What is the perimeter of a rectangle with width 10 inches in length 13 inches?
  10. Math

    the 3 sides of a triangle have lengths of (x+7) inches, (5x+6) inches, and (5x-3) inches. What is the length of the shortest side if the perimeter of the triangle is 43 inches

More Similar Questions