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?

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


Value of first integer = x = 10