Question

the perimeter of a rectangle is 91 cm.its length is (2x-1)cm and breadth is(x+9)cm.find its length and breadth.

Answer 1

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Perimeter= 2(l+b)
Length is given= (2x-1)
Breadth is given=(x+9)
Now putting in the formula

2(l+b)= 91
2(2x-1+x+9)=91
2(3x+8)=91
6x+16= 91
6x= 91-16
x= 75/6

Length= 2*75/6-1
=75-3/3
=72/3

Breadth= 75/6 +9
= 75+54/6
= 129/6
= 43/2

Verification
2(l+b)=91
2(72/3 + 43/2)=91
2(144+129/6)=91. (by taking lcm of 2 and 3 = 6)
2*273/6=91
91 = 91

Answer 2

Given that perimeter of a rectangle = 91cm.

Given that length of a rectangle = (2x-1)cm.

Given that breadth of a rectangle = (x+9)cm.

We know that perimeter of a rectangle = 2(l + b)

91 = 2((2x - 1 + x + 9))

91 = 2(3x + 8)

91 = 6x + 16

91 - 16 = 6x

75 = 6x

x = 75/6

x = 12.5cm.

Therefore the length = (2(12.5) - 1) = (25 - 1) = 24cm.

                  the breadth = (x + 9) = (12.5 + 9) = 21.5cm.


Verification:

91 = 2((2x - 1 + x + 9))

91 = 2(24 + 21.5)

91 = 2(45.5)

91 = 91.


Hope this helps!