The altitude divides the parallelogram into two right triangles, each with a hypotenuse of 10x - 1 and legs of 7x + 2 and 8x - 7. Applying the Pythagorean theorem to these triangles, we get The length of the altitude AD (height) of a parallelogram is 11/3 units.
To determine the length of the altitude AD (height) of a parallelogram, we can utilize the Pythagorean theorem. The altitude divides the parallelogram into two right triangles, each with a hypotenuse of 10x - 1 and legs of 7x + 2 and 8x - 7. Applying the Pythagorean theorem to these triangles, we get:
Triangle ABE:
A² = B² + C²
(10x - 1)² = (7x + 2)² + (8x - 7)²
100x² - 20x + 1 = 49x² + 28x + 4 + 64x² - 112x + 49
23x² - 92x + 50 = 0
Triangle CDE:
C² = D² + E²
(10x - 1)² = (7x + 2)² + (8x - 7)²
100x² - 20x + 1 = 49x² + 28x + 4 + 64x² - 112x + 49
23x² - 92x + 50 = 0
Solving for x, we get x = 7/3.
Substituting x = 7/3 into any of the two equations, we can find the length of AD:
AD = 10x - 1 = 10(7/3) - 1 = 28/3 - 1 = 11/3
Therefore, the length of AD is 11/3 units.