Question

The perimeter of rectangle is 90 cm and its area is 486 square find the dimension of rectangle

Answer 1

Given Data

Perimeter of rectangle = 90cm
Area of rectangle = 486sq cm

formula for perimeter of rectangle = 2(l+b)
formula for area of rectangle = l* b

where l = length of rectangle and b = breadth of rectangle.

we have to calculate the dimensions of rectangle means length and breadth

l*b = 486 sq cm---- equation 1
2(l+b) = 90
l+b = 45 cm --- equation 2

from equation 1
l= 486/b

substituting it in equation 2

486/b + b = 45
(486+ b^2)/b = 45
b^2 + 486 = 45b
b^2 -45b +486 = 0
it form a quadratic equation
general form is aX^2 +bX +c =0
compare it with general form

A= 1, b = -45 And c = 486

if we substitute in the attached formula. we will get the value of b
the value of b are 27 or 18

length = 486/b
length = 486/27= 18 or
length = 486/18= 27

so the dimensions of the rectangle are 27cm and 18 cm

Hope it helps you
Thank you!