Question

The smaller side of a rectangle is 6 cm less than that of it's larger side. If it's perimeter is 28 cm .
(a) what is the sum of the lengths of lager and smaller sides?
(b) what are the length of the sides?​

Answer 1

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Answer 2

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Let the lengths of each side of the smaller square be x cm and that of the larger square be y cm.

Then, area of the smaller square=x

2

cm

2

y

2

−2x

2

=14....(i)

2y

2

+3x

2

=203....(ii)

From (i) we have

y

2

=14+2x

2

Substituting this value of y

2

in (ii) we get

⇒28+4x

2

+3x

2

=203⇒7x

2

=203−28

⇒7x

2

=175⇒x

2

=25⇒x=5cm

Putting x=5 in (i) we get

y

2

−2×5

2

=14⇒y

2

=64⇒y=8

Hence the lengths of the sides of the square are 5cm and 8cm respectively