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11 Algebra-expression for the area of the rectangle

Unit 2.7 More expanding and factorising
The problem

A rectangular piece of paper has length  (x +5) cm and width ( x +2 ) cm. 

A square with sides of length, x cm is removed. 

a) Write an expression for the area of the rectangle before the square is cut out. Expand the brackets.

b) Write an expression for the shaded area

c) Find x if the shaded area is 31cm2.

 

The solution

a) Expression for the area of the rectangle before the square is cut.

( x + 5) ( x + 2) a) (x + 5) ( x +2) =x2 +7x +10

b) Expression of shaded area   ( x2 + 7x +10 ) -x2 = x2 + 7x +10 -x2  = 7x +10.c) Find x if the shaded area is 31 cm2.   7x + 10 = 31 ⇒7x = 31-10 =21⇒7x = 21⇒x = 217= 3⇒x =3.

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Ruhi Quadri Published on 06 Nov 2020
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