Question

a rectangle 9cm long is equal in area to a square which has a perimeter of 24cm. find the width of the rectangle

Answer 1

Answer:

breadth = 4

Step-by-step explanation:

perimeter of square =4×side =24

side =24÷4

side = 6 cm

area of square =6×6=36

area of rec.= L×B

36=L×B

36=9×B

36÷9=B

4=B

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Answer 2

Answer:

width= 4cm

Step-by-step explanation:

How?

Firstly, the perimeter of a square = 4l

and from question P=24cm

∴ P = 24cm = 4l

$24 = 4l \\divide both sides by 4\\\frac{24}{4} = \frac{4l}{4}\\Therefore, 6 = l; length of square is 6cm.$

length of square = 6cm

But, Rectangle area = Square area

and area of a square is $l^{2}$

∴ $A$ = $6^{2} = 36cm$

recall, Rectangle area = Square area

and area of rectangle is L×B

= A= 9 × B

= 36 = 9B

= $B = \frac{36}{9} \\\\B = 4cm$