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kykrilka [37]
3 years ago
9

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 recta

ngle.​
Mathematics
1 answer:
devlian [24]3 years ago
3 0

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 <em>(</em><em>expand</em><em>)</em>

W² -28W +171= 0 <em>(</em><em>bring</em><em> </em><em>everything</em><em> </em><em>to</em><em> </em><em>one</em><em> </em><em>side</em><em>)</em>

(W -19)(W-9)= 0 <em>(</em><em>factorise</em><em>)</em>

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.

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