Question

WITH SOLUTIONS PLEASE HELP ASAP. THANK YOU IN ADVANCE. Question=The perimeter of a rectangle is 90 centimeters. The width of the rectangle can be represented by (x + 2), and its length can be represented by (3x - 5).
What are the dimensions of this rectangle in centimeters? Options =
A ) With = 10 and length = 25
B )With = 12 and length = 29
C )With = 14 and length = 31
D )With = 16 and length = 32

Answer 1

Width = (x + 2)
Length = (3x - 5)

Perimeter = 90 cm

Perimeter of a rectangle = 2(l + b)
= 2( 3x - 5 + x + 2)
= 2(4x - 3)
= 8x - 6

90 = 8x - 6
8x = 96
x = 96/8 = 12 cm

So, length = (3x - 5) = 36 - 5 = 31
Width = x + 2 = 12 + 2 = 14 cm


So, the answer is (C)

Answer 2

Perimeter of the rectangle= 90 cm
its length = (3x-5)
its breadth = (x+2)

 perimeter of the rectangle =   2(l+b) 
                        ⇒ 2{(3x-5) + (x+2)} = 90
                        ⇒2( 3x-5 +x+2) = 90
                        ⇒ 2( 4x-3)  = 90
                        ⇒ 8x - 6  =90
                        ⇒ 8x = 90+6
                        ∴ x = 96/8= 12
so x= 12

length of the rectangle=  3x-5
                                   = 3*12 - 5
                                   = 36-5
                                   = 31
breadth(width) of the rectangle= x+2
                                      = 12+2
                                      = 14
so width = 14 and length = 31

so C) is the answer.