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.

step-by-step :

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for