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zvonat [6]
3 years ago
11

The length of a rectangle is twice its width. Find its area, if its perimeter is 7 1/3 cm The area of the rectangle is _sq. cm.

Mathematics
1 answer:
Harman [31]3 years ago
7 0

Answer:

The area of rectangle is 2\frac{80}{81}\ cm^2

Step-by-step explanation:

we know that

The perimeter of a rectangle is equal to

P=2(L+W)

we have

P=7\frac{1}{3}\ cm=7+\frac{1}{3}=\frac{22}{3}\ cm

so

\frac{22}{3}=2(L+W)

\frac{11}{3}=(L+W) ----> equation A

Remember that

The length of a rectangle is twice its width.

so

L=2W ----> equation B

substitute equation B in equation A

\frac{11}{3}=(2W+W)

solve for W

W=\frac{11}{9}\ cm

Find the value of L

L=2(\frac{11}{9})

L=\frac{22}{9}\ cm

<em>Find the area of rectangle</em>

A=LW

substitute the values

A=(\frac{22}{9})(\frac{11}{9})

A=\frac{242}{81}\ cm^2

Convert to mixed number

\frac{242}{81}\ cm^2=\frac{162}{81}+\frac{80}{81}=2\frac{80}{81}\ cm^2

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01. Se tienen los angulos consecutivos AOB, BOC y COD. se cumple m&amp; AOC=125° m <br>​
Citrus2011 [14]

La diferencia entre los ángulos <em>AOB</em> y <em>COD</em> del sistema de tres ángulos <em>consecutivos</em> es igual a 25°.

La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°.

<h3>Cómo analizar tres ángulos consecutivos</h3>

Por la geometría Euclídea conocemos que un conjunto de ángulos cuando comparten entre cada par de ángulos vecinos comparten el mismo vértice y la misma semirrecta.

De acuerdo con el enunciado, tenemos las siguientes condiciones:

∠AOB + ∠BOC = 125°   (1)

∠BOC + ∠COD = 100°  (2)

Por (1) y (2) tenemos las siguiente identidad:

∠AOB - 25° = ∠COD

∠AOB - ∠COD = 25°

La diferencia entre los ángulos <em>AOB</em> y <em>COD</em> del sistema de tres ángulos <em>consecutivos</em> es igual a 25°. \blacksquare

En el segundo caso, tenemos el siguiente sistema:

∠AOB = ∠BOC + ∠COD     (3)

∠AOB + ∠BOC - ∠COD = 40°     (4)

Por (3) y (4) tenemos la siguiente identidad:

2 · ∠BOC = 40°

∠BOC = 20°

La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°. \blacksquare

Para aprender más sobre ángulos, invitamos cordialmente a ver esta pregunta verificada: brainly.com/question/21209282

8 0
2 years ago
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