Question

The area of a rectangular carpet is
120m² and its perimeter is 46 m. the
length of its diagonal is :​

Answer 1

Answer:

17 m

Step-by-step explanation:

Given that perimeter of a rectangular carpet = 46m. Given that Area of a rectangular carpet = 120m^2. = 17. Therefore the length of the diagonal = 17m.

Answer 2

FINAL ANSWER:-

diagonal is 17 cm

FORMULA USED:-

area of rectangle = L×B

perimeter of rectangle = 2(L+B)

Pythagoras theorem = hypotenuse²=base²+perpendicular²

SOLUTION:-

area of rectangle = 120m²

perimeter of rectangle = 46m

∴ L×B=120....(i)

  2(L+B)=46....(ii)

  L=23-B....(iii)

now let put eq(iii) in eq(i)

∴we get,

(23-B)×B=120

23B-B²=120

B²-23B+120=0

b =(23+√49)/2=(23+7)/2= 15

or

b =(23-√49)/2=(23-7)/2= 8

→lets take b as 8 ,

so lets put it in eq(ii)

∴we get

2(L+8)=46

2L+16=46

2L=30

L=$\frac{30}{2}$

L=15cm

⇒ now using Pythagoras theorem we get

$h^{2}=b^{2}+p^{2}\\h^{2}=15^{2}+ 8^{2} \\h^{2}=289\\h=\sqrt{289}\\h=17cm$

diagonal is 17 cm