Question

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

Answer 1

Answer:

Length of Diagonal=17cm

Step-by-step explanation:

lb =area

120=lb

b=120/l

2(l+b)=46=Perimeter

l+b=23

l+120/l=23

$l^{2}$+120=23l

$l^{2}$-23l+120=0

$l^{2}$-15l-8l+120=0

l(l-15)-8(l-15)=0

(l-15)(l-8)=0

Hence  length is 15m and  breadth is 8m

By pythogoras theorum,

$(Diagonal)^{2}$=$(Length)^{2}$+$(Breadth)^{2}$

$(Diagonal)^{2}$=$15^{2}$+$8^{2}$

$(Diagonal)^{2}$=225+64

$(Diagonal)^{2}$=289

Taking root,

Diagonal=±17cm

Diagonal=17cm(Measurements cannot be negative)

Length of Diagonal=17cm

Hope it helps...

Answer 2

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.