1. In trapezoid ABCD with AB || CD, the diagonals intersect at point P. The line passing through P and parallel to AB intersects AD and BC at points E and F, respectively. Given that AB = 6 and CD = 12, find EP and FP.
2. The lengths of two sides of an isosceles triangle are 10 and 12 centimeters. Find all possible values of the area of this triangle.
3. The area of trapezoid ABCD, with AD||BC, is 164. The altitude is 8, AB is 10, and CD is 17. Find all possible values of the length of side BC, in centimeters.
+128474 2. The lengths of two sides of an isosceles triangle are 10 and 12 centimeters. Find all possible values of the area of this triangle.
Either the remaining side is 10 or it is 12
If it is 10
Semi-perimeter, S = (10 + 10 + 12) / 2 = 16
Area = sqrt [ S ( S - A) (S - B) (S - C) ] where A,B,C are the side lengths
Area = sqrt [ 16 ( 16 - 10) (16-10)(16-12) ] = sqrt [ 16 * 6 * 6 * 4 ] = sqrt [ 16 * 36 *4 ] = 4*6*2 = 48
If it is 12
Semi-perimeter = (10 + 12 + 12) / 2 = 17
Area = sqrt [ 17 (17 -12) (17-12) ( 17 -10) ] = sqrt [ 17 * 5 *5 * 7 ] = sqrt [ 119 * 25 ] = 5sqrt (119)
