A rectangle has a length of 11 meters less than 10 times its width. If the area of the rectangle is 9888 square meters, find the length of the rectangle.

Question

Mathematics

Jersey

15 February, 06:18

A rectangle has a length of 11 meters less than 10 times its width. If the area of the rectangle is 9888 square meters, find the length of the rectangle.

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Answers (1)

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Mateo Lopez · Answer 1

Step-by-step explanation:

The Length,

L

=

284

f

t

.

Explanation:

Given:

Rectangle

Area,

A

=

8804

f

t

2

let W bet he width of the rectangle

L be the length of the rectangle

L

=

10

W

-

26

E

q

u

a

t

i

o

n

1

substitute to

e

q

u

a

t

i

o

n

2

A

=

(

L

)

(

W

)

e

q

u

a

t

i

o

n

2

A

=

(

10

W

-

26

)

(

W

)

8804

=

(

10

W

-

26

)

(

W

)

factor

8804

=

2

(

5

W

-

13

)

(

W

)

divide both sides by 2

4402

=

(

5

W

-

13

)

(

W

)

4402

=

5

W

2

-

13

W

transposing 4402 to the right side of the equation

0

=

5

W

2

-

13

W

-

4402

by quadratic formula

W

=

-

(

-

13

)

+

√

(

-

13

)

2

-

4

(

5

)

(

-

4402

)

2

(

5

)

W

=

[

13

+

√

169

+

88040

]

10

W

=

13

+

(

√

88209

)

10

W

=

13

+

297

10

W

=

310

10

W

=

31

ft

Thus,

L

=

10

W

-

26

=

10

(

31

)

-

26

L

=

284

f

t

.

answer

W

=

-

(

-

13

)

-

√

-

(

-

13

2

)

-

4

(

5

)

(

-

4402

)

2

(

5

)

this is discarded since this will yield a negative