Question

A path 5m wide rins along inside a rectangular field . The lengh of the rectangular field os three times the breadth of the field . If the area of the path is 500 meter square , then the length and breadth of the field​

Answer 1

Answer:

Reference of Image is in Attachment :

Let the Breadth of Rectangular Filed a m and, length will be 3a m

⋆ Now In Rectangle EFGH :

⇝Length (EF) = (3a - 5 - 5) = (3a - 10) m

⇝Breadth (FG) = (a - 5 - 5) = (a - 10) m

• According to the Question Now :

⇒ Ar. of Path = Ar. of ABCD - Ar. of EFGH

⇒ Ar. of Path = (AB × BC) - (EF × FG)

⇒ 500 = (3a × a) - {(3a - 10) × (a - 10)}

⇒ 500 = 3a² - (3a² - 30a - 10a + 100)

⇒ 500 = 3a² - 3a² + 30a + 10a - 100

Both 3a² will be cancelled

⇒ 500 + 100 = 40a

⇒ 40a = 600

Dividing Both term by 40

⇒ a = 15 m

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◗ Breadth = a = 15 m

◗ Length = 3a = 3(15) = 45 m

∴ therefore, Length will be 45 m and Breadth will be 15 m of rectangular field.