The area of a rectangle is 504 square meters. if the perimeter is 90 meters, find the length and width of the rectangle.

Length =24m and width = 21m

Step-by-step explanation:

Given,

Area of rectangle, A = 504 m^2

Perimeter of rectangle, P = 90 m

Since we know, A = Length * width  and  P = 2(Length + width)

So, A = L * w

=> 504 = L*w     (1)

And P = 2(L + w)

=> 90 =2( L + w)    (2)

Plug L =504/w in equation 2

i.e.  90 = 2( 504/w + w)

or 45 = 504/w  +  w

or 45 = (504 + w^2 ) / w

or 45w = 504 + w^2

or w^2 - 45w + 504 = 0

On solving above quadratic equation we get:

w = 21 or 24

So we take width , w= 21 meter

Then length will be, L =504/21 =24 meter

Hence length and width of rectangle are 24m and 21m respectively.

x = 2

Make the opposite sides equal to each other

Step-by-step explanation:

in a parallelogram each 2 opposite sides = each other, they have THE EXACT SAME VALUE. so to solve this you only need to make the expressions of the opposite sides equal to each other. Then you can use algebra to solve for x.

2x + 5 = 4X + 1

X = 2