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nadezda [96]
3 years ago
5

The figure is a parallelogram. One diagonal measures 28 units.

Mathematics
2 answers:
Kaylis [27]3 years ago
8 0

Answer:

The parallelogram is not rectangle because the sides of the parallelogram do not meet at right angles.

Step-by-step explanation:

Given the parallelogram with sides 20 and 21 units with diagonal length 28 units.

we have to tell it is a rectangle or not.

The given parallelogram is rectangle if the angle at vertices are of 90° i.e the two triangle formed must be right angles i.e it  must satisfy pythagotas theorem

28^2=20^2+21^2

784=400+441=881

Not verified

∴ The sides of the parallelogram do not meet at right angles.

Hence, the parallelogram is not rectangle because the sides of the parallelogram do not meet at right angles.

Option B is correct

astraxan [27]3 years ago
3 0

Answer:

B. No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

Step-by-step explanation:

Law of cosines: a^2 = b^2 +c^2 - 2*b*c*cos(A)

Let's call

a = the side which is 28 units length

b = the side which is 21 units length

c = the side which is 20 units length  

A = the angle formed between sides b and c

Solving the formula for A, we get

a^2 = b^2 +c^2 - 2*b*c*cos(A)

2*b*c*cos(A)  = b^2 +c^2 - a^2

cos(A)  = (b^2 +c^2 - a^2)/(2*b*c)

A = arccos[(b^2 +c^2 - a^2)/(2*b*c)]

A = arccos[(21^2 +20^2 - 28^2)/(2*21*20)]

A = 86.1°

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