Question

Perimeter of rectangle= perimeter of square= 160cm
100- area of rectangle= area of square= 1600cm². Find the length of rectangle

Answer 1

Answer:

30cm or 50cm

Step-by-step explanation:

let, length of rectangle=l

      breadth of rectangle=b

      side of the square = a

                       

PERIMETER:

perimeter of rectangle ⇒2(l+b) = 160cm

                                      ⇒l+b=160/2

                                      ⇒l+b=80cm

perimeter of a square  ⇒4(a) = 160cm

                                     ⇒ a = 160/4

                                     ⇒ a = 40cm

AREA:

area of square = $cm^{2}$

now  given that,

⇒area of rectangle - 100 = 1600

⇒ l*b - 100=1600

⇒ l*b = 1600-`100

⇒ l*b = 1500

now putting  b = 80 - l from perimeter in l*b = 1500

⇒ l*(80-l) = 1500

⇒ 80l - l^2 = 1500

⇒ l^2 - 80l + 1500 = 0

by solving the above equation we get,

length of the rectangle is equal to = 30cm or 50cm