A new homeowner needs to determine the length of his rectangular backyard before he goes to the store for

fencing. He knows that the area of the yard is 51 square meters and that the width is 5.2 meters longer

than the length. Which equation could be solved to determine the dimensions of the backyard, where the length

is / and the width is w?

0=w2+5.2w -51

o

0=12+5.21-51

4w + 10.4 = 51

о

41 +10.4 = 51

Question

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Omm2 Omm2 · Answer 1 · 2021-02-12T13:02:55+01:00

Answer:

The equation used to solved to determine the dimensions of the backyard is 51 = 4w - 10.4

Step-by-step explanation:

As given,

The backward is rectangular in shape

Also , we know that

Area of rectangle = 2 ( Length + Breadth )

Also, given,

Breadth of the backyard = 5.2 + Length of the backyard

Let

length of the backyard = l

Breadth of the backyard = w

∴ we get

w = 5.2 + l

⇒l = w - 5.2

and

Area = 2 ( l + w)

⇒51 = 2( w - 5.2 + w)

⇒51 = 2 ( 2w - 5.2)

⇒51 = 4w - 10.4

So, the equation used to solved to determine the dimensions of the backyard is 51 = 4w - 10.4

By solving we get

4w = 51 + 10.4

⇒4w = 61.4

⇒w = [tex]\frac{61.4}{4}[/tex] = 15.35

⇒ w = 15.35

⇒ l = w - 5.2 = 15.35 - 5.2 = 10.15

⇒l = 10.15

So the dimensions of the backyard = l × b = 10.15 m × 15.35 m