in a parallelogram, the adjacent sides are 39 cm and 25 cm respectively and the diagonals of the parallelogram are 34 cm in length find the area of the parallelogram
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A Parallelogram Has Sides of Lengths 39 and 25 and a Diagonal of Length 34. So, What Makes It So Special!
Thanks to TC's inspired challenge to our readers in a comment on the Medians of a Triangle post, I've decided to expand it into an investigation for our readers and students (geometry with some trig needed).
Consider a parallelogram whose sides have lengths 39 and 25 and with one diagonal of length 34.
(a) Explain why this parallelogram is unique, i.e., all parallelograms with these characteristics are congruent. Why was it not necessary to specify that the 'shorter' diagonal was given?
(b) A parallelogram has sides of lengths a and b and diagonals of lengths c and d. Use the Law of Cosines to show that
c2 + d2 = 2(a2 + b2).
(c) Determine the length of the other diagonal. As an alternative, how would you do it without the formula in (b)?
(d) Determine the area of this parallelogram.
Thanks to TC's inspired challenge to our readers in a comment on the Medians of a Triangle post, I've decided to expand it into an investigation for our readers and students (geometry with some trig needed).
Consider a parallelogram whose sides have lengths 39 and 25 and with one diagonal of length 34.
(a) Explain why this parallelogram is unique, i.e., all parallelograms with these characteristics are congruent. Why was it not necessary to specify that the 'shorter' diagonal was given?
(b) A parallelogram has sides of lengths a and b and diagonals of lengths c and d. Use the Law of Cosines to show that
c2 + d2 = 2(a2 + b2).
(c) Determine the length of the other diagonal. As an alternative, how would you do it without the formula in (b)?
(d) Determine the area of this parallelogram.
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area of parallelogram =length ×breadth. 39×25=975cm2
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