Since the perimter is 40, each side is 10.
So, the area is 5.6*10 = 56.
The area is also half the product of the diagonals. So, to get the other diagonal d,
56 = 1/2 * 7 * d
d = 16
The perimeter of a rhombus is 40 cm and the distance between a pair of parallel side is 5.6 cm. If the length of one of its diagonals is 7 cm, find the length of the other diagonal.
4 answers
Each side length is the same (since it is a rhombus) and therefore 10 cm. The diagonals intersect at right angles, forming four congruent right trangles.
The sides of those triangles are
5, 3.5 and sqrt[5^2 - 3.5^2] = 3.571, making the other diagonal length 2*3.571 = 7.141
You have been given more information than necessary to solve the problem. The distance between pairs of parallel sides is inconsistent with the lengths of diagonals.
The distance from the centroid to one side, d, must be such that
(1/2)*10*d = (1/2)*7*7.141
Therefore d = 4.999 and the distance between parallel faces is 9.997
Your provided data is inconsistent with a rhombus.
The sides of those triangles are
5, 3.5 and sqrt[5^2 - 3.5^2] = 3.571, making the other diagonal length 2*3.571 = 7.141
You have been given more information than necessary to solve the problem. The distance between pairs of parallel sides is inconsistent with the lengths of diagonals.
The distance from the centroid to one side, d, must be such that
(1/2)*10*d = (1/2)*7*7.141
Therefore d = 4.999 and the distance between parallel faces is 9.997
Your provided data is inconsistent with a rhombus.
The data given for the problem contradicts each other and does not make sense.
drwls pointed out correctly that we would get 4 congruent right-angled triangles,
the hypotenuse would be 10, one side is 3.5, let the other side be x
x^2 + 3.5^2 = 10^2
x = √87.75 or appr. 9.367
making the other diagonal 18.734
and then the area of the rhombus would be
(1/2)(7(18.734) or 65.57
So far I have ignored the information that the distance between one set of parallel sides is 5.6
As Steve has done, that way the area would have to be (10(5.6) or 56 , which contradicts my earlier calculation of the area.
So we have a bogus question.
drwls pointed out correctly that we would get 4 congruent right-angled triangles,
the hypotenuse would be 10, one side is 3.5, let the other side be x
x^2 + 3.5^2 = 10^2
x = √87.75 or appr. 9.367
making the other diagonal 18.734
and then the area of the rhombus would be
(1/2)(7(18.734) or 65.57
So far I have ignored the information that the distance between one set of parallel sides is 5.6
As Steve has done, that way the area would have to be (10(5.6) or 56 , which contradicts my earlier calculation of the area.
So we have a bogus question.
Yes, I agree with Reiny that I did the math wrong when computing the other diagonal. However, the statement that the set of dimensions are incompatible with a rhombus remains valid.
1 answer