Question

A piece of copper wire which is 56cm long is bent to form a rectangle of area 171cm².find the length and the width of this rectangle.​

Answer 1

Answer:

Length= 19cm

Width= 9cm

Step-by-step explanation:

let the length of the rectangle be L cm and its width be W cm.

Perimeter of rectangle= 56cm

2L +2W= 56

L +W= 56 ÷2

L +W= 28

L= 28 -W -----(1)

Area of rectangle= length ×width

LW= 171 -----(2)

Susbt. (1) into (2):

W(28 -W)= 171

28W -W²= 171 (expand)

W² -28W +171= 0 (bring everything to one side)

(W -19)(W-9)= 0 (factorise)

W-19=0 or W-9=0

W= 19 or W= 9

Subst into (1):

L=28 -19 or L= 28 -9

L=9 or L= 19

Since we usually take the longer side of the rectangle to be its length, L= 19 and hence W=9.

Therefore its length is 19cm and its width is 9cm.