Answer:
x = 3/2
Step-by-step explanation:
We can use ratios to solve
6 6+x
-------- = -----------
4 5
Using cross products
6*5 = 4 * (6+x)
30 = 24 + 4x
Subtract 24 from each side
30 -24 = 24+4x-24
6 = 4x
Divide each side by 4
6/4 = 4x/4
3/2 = x
Area of Rectangle = Width × Length
Vegetable Garden
Width = 20
Length = 45
Area of Vegetable Garden = 20×45=900 Sq ft
Area of Entire Garden = Width × Length
Width = 20 + 2x
Length = 45 + 2x
Area = (20 + 2x)(45 + 2x)
(2x + 20)(2x + 45)
4x^2 + 90x + 45x + 900
Area of Entire Garden = 4x^2 + 135x + 900
Area of Flower Garden = Area of Entire Garden - Area of Vegetable Garden
(4x^2 + 135x + 900) - (20 × 45)
4x^2 + 135x + 900 - 900
Area of Flower Garden = 4x^2 + 135x
Vertical angles are equal, so
.. 3x +8 = 5x -20
.. 28 = 2x . . . . . . . . add 20-3x
.. 14 = x . . . . . . . . . . divide by 2
Each of the vertical angles is 3*14 +8 = 50°, so the supplementary one is 130°.
.. 5*14 +4y = 130
.. 4y = 60 . . . . . . . . subtract 70
.. y = 15 . . . . . . . . . . divide by 4
The values of interest are
.. x = 14
.. y = 15
