Perimeter of a rectangle Hie perimeter P of a rectangle with

Perimeter of a rectangle. Hie perimeter P of a rectangle with a fixed width is a linear function of its length. The perimeter is 28 inches when the length is 6.5 inches, and the perimeter is 36 inches when the length is 10.5 inches. Write P as a linear function of L What is the perimeter when L = 40 feet1 What is the fixed width of the rectangle0

Solution

Permieter is a linear function of length:

P = ml + c   ;

(l, P) --- (6.5 , 28)

(l,P) ---( 10.5 , 36)

m = (36-28)/(10.5 -6.5) = 8/4 = 2

P =2l+c : find c

36 = 10.5*2 +c ----> c = 36 - 21 = 15

So, P = 2l +15

Permeter when l = 40 feet: P = 2*40 +15 = 95 feet

width =( P - 2l)/2 = ( 28 - 2*6.5)/2 = 7.5 feet