Question

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

Is the figure a rectangle? Explain.

A. No, it is not a rectangle because the diagonals are congruent.
B. No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.
C. Yes, it is a rectangle because the diagonals are congruent.
D. Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.

Answer 1

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

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°

Answer 2

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

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