Posted by qwerty123 on Monday, March 21, 2011 at 6:30pm.
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
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.
Related Questions
geometry - Triangle ABC and triangle XYZ are similar. If AB, BC, and AC are 7 ...
geometry - The sum of the lengths of the sides of triangle ABC is 25 in. The ...
Math - The sum of the lengths of the sides of triangle ABC is 38in. The length ...
geometry - Two sides of a triangle measure 4 inches and 9 inches. Determine ...
Geometry - The lengths of the sides of a triangle are 3,5, and 7 inches. How ...
geometry - what is the perimeter of a triangle whose sides measure 7 3/4 inches,...
geometry - In triangle ABC, if line BC is one inch longer than line AB, line AC ...
math - Let PSR be a triangle. Let A, B, C be the midpoints of the sides PS, PR ...
Algebra 2 - Can you double check my answer The lengths of the sides of a ...
Geometry - the lengths of 2 sides of a triangle are 2 inches and 10 inches. find...
For Further Reading
