A diagonal of a parallelogram is also its altitude. What is the length of this altitude, if the perimeter of the parallelogram i
s 50 cm, and the length of one side is 1 cm longer than the length of the other?
1 answer:
Answer:
The length of this altitude is 5 cm.
Step-by-step explanation:
The length of the altitude = ?
Given the diagonal forms the altitude of the parallelogram. The figure is shown in image.
Given
The perimeter of the parallelogram = 50 cm
The length of one side is 1 cm longer than the length of the other.
Thus,
Let one side (a) is x cm, The other side (b) be (x + 1) cm
<u>Perimeter of parallelogram = 2(a + b) = 2(x +(x + 1)) = 4x + 2 = 50 cm</u>
Thus,
x = AB = CD = 12 cm
x + 1 = BC = AD = 13 cm
Using Pythagorean theorem to find the length of the altitude as:
ΔABC is a right angle triangle.
AB² + AC² = BC²
<u>AC² = 13² - 12² = 5 cm</u>
<u>The length of this altitude is 5 cm.</u>
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