Question

9) The base and the height of a rectangle are represented by the expressions below.

Base= x+4 Height= x-6
The perimeter of the rectangle 88 units. Find the lengths of the base and the height of the rectangle.

10) The sum of three consecutive even integers is 36. Let x represent the first integer,
x +2 represent the second integer, and x +4 represent the third integer. what is the first integer?

Answer 1

9 :


Given,
Perimeter = 88 units
Base = x + 4
Height = x - 6





= > Perimeter of Rectangle = 2( base + height )


= > 88 = 2{ ( x + 4 ) + ( x - 6 ) }

= > 88 / 2 = { x + 4 + x - 6 }

= > 44 = 2x - 2

= > 46 = 2x

= > 46 / 2 = x

= > 23 = x





Therefore,


Length of base = ( x + 4 ) units = ( 23 + 4 ) units = 27 units

Length of height = ( x - 6 ) units = ( 23 - 6 ) units = 17 units





10 :




Given,
First integer = x
Second integer = x + 2
Third Integer = x + 4




Given that the sum of all integers is 36


= > ( x ) + ( x + 2 ) + ( x + 4 ) = 36

= > x + x + 2 + x + 4 = 36

= > 3x + 6 = 36

= > 3x = 30

= > ( 3x ) ÷ ( 3 ) = ( 30 ) ÷ ( 3 )

= > x = 10






`image`
Value of first integer = x = 10