SOLUTION: (1)Find the value of an isosceles triangle with its side ABC such that line AB is 14cm,line AC is (7y-3) and line BC is 5(y+1).(2)find the value of y.(3)find the height of triangle

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Question 1036270: (1)Find the value of an isosceles triangle with its side ABC such that line AB is 14cm,line AC is (7y-3) and line BC is 5(y+1).(2)find the value of y.(3)find the height of triangle ABC.(4)Hence complete the area of triangle ABC.

Answer by Aldorozos(172) (Show Source):
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Since it is isosceles triangle 5(y+1) =7y-3 solving this equation gives us y = 4
If replace 4 in one of the equations to calculate the side of the triangle
7*4-3 = 25 = side of the triangle.
Now we use Pythagorean Theorem to calculate the height of the triangle. We know the base is 11 and we know the side is 25. We divide the base to 1/2 to have two right triangles. By doing so, we can apply the theorem. We will have two triangles with the base of 5.5 and hypotenuse of 25.
The height of the triangle is 25^2 - 5.5^2 = height^2 = 594.75. Therefore the height is the square root of 594.75 which is 24.39
The area of one of the right angles is 5.5*24.39/2 and the area of both right angles which is the same as the area of the isosceles triangle is twice which means 5.5*24.39