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3 years ago

A rectangle has an area of 21x+81. If the width is 3 units, what is the length of the rectangle

Mathematics

1 answer:

Oxana [17]3 years ago

6 0

Answer:

(7x + 27) units

Step-by-step explanation:

A rectangle is a quadrilateral (has four sides) in which opposite sides are equal and parallel, also all the angles are equal. The area of a rectangle is given as:

Area = Length × Width

Given that the area of the rectangle is 21x + 81 and the width is 3 unit, to find the length of the rectangle, we have to use the formula of the area and then get the length. Therefore:

Area = Length × Width

21x + 81 = Length × 3

Length = (21x + 81) /3

Length = 7x + 27

The length of the rectangle is 7x + 27 units

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Holly spends 7 3/5 hours in school each day. Her lunch is 1/2 hour long, and she spends 7/10 of a hour switching classes. The re

Ira Lisetskai [31]

y = 7 + 3/5
y = 35/5 + 3/5
y = 38/5
y = 2*(38/5)
y = 76/10
---
lunch time:
z = 1/2
z = 5*(1/2)
z = 5/10
---
time switching classes:
w = 7/10
---
y - 6x - z - w = 0
6x = y - z - w
x = (y - z - w)/6
x = (76/10 - 5/10 - 7/10)/6
x = (76 - 5 - 7)/(10*6)
x = (64)/(10*6)
x = (2*2*2*2*2*2)/(2*5*2*3)
x = (2*2*2*2)/(5*3)
x = 16/15

x = 1.0666666666
---
check:
y = 7 + 3/5
y = 7.6
z = 1/2
z = 0.5
w = 7/10
w = 0.7
y - 6x - z - w = 0
6x = y - z - w
x = (y - z - w)/6
x = (7.6 - 0.5 - 0.7)/6
x = 1.0666666666

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3 years ago

The length of a rectangle is 7 meters more than four times its width if the area of the rectangle is 650 square meters, find the

mrs_skeptik [129]

Let the width be x.
Width = x
Length = 4x + 7

The area is 650 m²

x(4x + 7) = 650
4x² + 7x - 650 = 0

Using quadratic formula:
$x = \dfrac{-b \pm \sqrt{b^2 - 4ac} }{2a}$

a = 4, b = 7, c = -650

$x = \dfrac{-7 \pm \sqrt{7^2 - 4(4)(-650} }{2(4)}$

$x = 11.9 \ or\ x = -13.7 \text {(rejected, length cannot be negative)}$

Width = 11.9m
Length = 4(11.9) + 7 = 54.6m

Answer: Length = 54.6m and width = 11.9m

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