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Ratio of Area of Rectangle ABEF to Rectangle ACDF is 2 : 3

Area of rectangle ABEF is 10√41 units²

Perimeter of rectangle BCDE is ( 10 + 2√41 ) units²

Step-by-step explanation:

Given: ABEF and BCDE and ACDF are rectangles.

          coordinates of F( 5 , 2 ) , E( 11 , 10 ) , D( 14 , 14 ) and A( 0 , 6 )

To find: Ratio of Area of Rectangle ABEF to Rectangle ACDF

             Area of rectangle ABEF

             Perimeter of BCDE.

We know that, Area of Rectangle = Length × Width

In rectangle ABEF

length = FE =

Width = FA

Area of Rectangle ABEF = FE × FA = ( 10 × FA ) units²

In rectangle ACDF

length = FD =

Width = FA

Area of Rectangle ACDF = FD × FA = ( 15 × FA ) units²

Thus, Ratio of Area of Rectangle ABEF to Rectangle ACDF is 2 : 3

In rectangle ABEF

length = FE = 10 units    (from above)

Width = FA =

Area of Rectangle ABEF = FE × FA = 10 × √41 = 10√41 units²

Thus, Area of rectangle ABEF is 10√41 units²

In rectangle BCDE

length = DE =  

Width = CD = FA = √41 units

Perimeter of Rectangle BCDE = 2 × ( DE + CD ) = 2 × (5 + √41) = ( 10 + 2√41 ) units²

Thus, Perimeter of rectangle BCDE is ( 10 + 2√41 ) units²

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3