1.

the area of a rectangular carpet is 120 metre square and its perimeter is 46 metre the length of its diagonal is ​

Answer»

ANSWER:

The length of the diagonal is 17 m.

Step-by-step explanation:

Given :

AREA = 120 m²

Perimeter = 46 m

To find :

Length of the Diagonal

Solution :

Let the -

  • Length as l
  • Breadth as b

\rule{300}{1.5}

★ Area = Length × Breadth

⇒ l × b = 120

⇒ lb = 120

⇒ b = 120/l

\rule{300}{1.5}

★ Perimeter = 2(Length + Breadth)

⇒ 2(l + b) = 46

⇒ l + b = 46/2

⇒ l + 120/l = 23

⇒ l² + 120 = 23l

⇒ l² - 23l + 120=0

⇒ l² - 15l - 8L + 120 = 0

⇒ (l - 15) - 8(l - 15) = 0

⇒ (l - 15)(l - 8) = 0

Length is 15m

 Breadth is 8m

\rule{300}{1.5}

★ Diagonal -

By Pythogoras THEORUM,

(Hypotenuse)² = (BASE)² + (Height)²

⇒ (Hypotenuse)² = (15)² + (8)²

⇒ (Hypotenuse)² = 225 + 64

⇒ (Hypotenuse)² = 289

⇒ Hypotenuse = \sf{\sqrt{289}}

⇒ Hypotenuse = 17 m

Diagonal = 17 m.

Therefore, the length of the diagonal is 17 m.



Discussion

No Comment Found

Related InterviewSolutions