The length of the shorter side of a parallelogram is 29 cm. Perpendicular line segment, which goes through the point of intersec
tion of the diagonals to the longer side divides this longer side into two segments: 33cm and 12cm. What is the area of the parallelogram?
1 answer:
By definition, a parallelogram is merely a quadrilateral. Its key characteristics are having two sets of parallel sides. Consequently, it would have two sets of equal lengths, denoted as a and b. A perpendicular bisector is the red line in the picture that bisects length b into two lengths while creating a right angle. The area of a parallelogram is
A = bh, where
b is the side that meets with h
h is the perpendicular height of the parallelogram
Since h is not known, we have to solve it first through applying the pythagorean theorem.
h = √29^2 - 12^2 = 26.4 m
Thus,
A = (12 cm + 33 cm)(26.4 cm)
A = 1,188 square centimeters
A = bh, where
b is the side that meets with h
h is the perpendicular height of the parallelogram
Since h is not known, we have to solve it first through applying the pythagorean theorem.
h = √29^2 - 12^2 = 26.4 m
Thus,
A = (12 cm + 33 cm)(26.4 cm)
A = 1,188 square centimeters
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If we let x and y represent length and width, respectively, then we can write equations according to the problem statement.
.. x = y +2
.. xy = 3(2(x +y)) -1
This can be solved a variety of ways. I find a graphing calculator provides an easy solution: (x, y) = (13, 11).
The length of the rectangle is 13 inches.
The width of the rectangle is 11 inches.
______
Just so you're aware, the problem statement is nonsensical. You cannot compare perimeter (inches) to area (square inches). You can compare their numerical values, but the units are different, so there is no direct comparison.
.. x = y +2
.. xy = 3(2(x +y)) -1
This can be solved a variety of ways. I find a graphing calculator provides an easy solution: (x, y) = (13, 11).
The length of the rectangle is 13 inches.
The width of the rectangle is 11 inches.
______
Just so you're aware, the problem statement is nonsensical. You cannot compare perimeter (inches) to area (square inches). You can compare their numerical values, but the units are different, so there is no direct comparison.