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scoray [572]
3 years ago
7

Huntington Park officials approved a rectangular plot of land for a Japanese Zen garden. Is it sufficient to know that opposite

sides of the garden plot are congruent and parallel to determine that the garden plot is rectangular? Explain
Mathematics
1 answer:
Sergeu [11.5K]3 years ago
4 0

Answer: No, it is not sufficient to know that opposite sides of the garden plot are congruent and parallel to determine that the garden plot is rectangular.


Step-by-step explanation:

1. You have the following information given in the problem:

- Opposite sides of the garden plot are congruent.

- Opposite sides of the garden plot are parallel.

2. Therefore, keeping the information above on mind, you can conclude that the description is about a parallelogram, but to determine that it is rectangular, you need to know that the four interior angles measure 90° and the diagonals are congruent.


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Granted that uppercase letters are the angles measurements and lowercase letters are the side lengths. I also was unable to round as I don't know to what decimal you need to round to.

First to find the measure of angle B, we must subtract A and C from 180

180-21-105=54

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Next, we can use the law of sines in order to find the measures of a and b

As a reminder, The law of sines is

\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

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\frac{b}{sin54}=\frac{5}{sin105} \\\\b=\frac{(5)sin54}{sin105}\\\\b=4.187780119

Next lets solve for a

\frac{a}{sin21}=\frac{5}{sin105} \\\\a=\frac{(5)sin21}{sin105}\\\\a=1.85504901

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