You design a tree house using a coordinate plane in which the coordinates are measured in feet. The vertices of the floor are (-2,-3),(-2,4),(5,4) and (5,-3) . Find the perimeter (in yards) and the area (in square yards).

Step-by-step explanation:

The vertices (-2, -3) and (-2, 4) are on the same vertical line and are separated by 4 - (-3), or 7, units.  The vertices (-2, 4) and (5, 4) are on the same horizontal line (y = 4) and separated horizontally by 5 - (-2), or 7, units.  If you can picture this in your mind, you'll see a 45-45-90 isosceles triangle with leg lengths 7 (there are two such legs).

The next thing to do is to calculate the length of the hypotenuse of this triangle.  Using the Pythagorean Theorem, we get:

d = √(7² + 7²) = 7√2 ft.

The perimeter of this triangle is thus 7 ft by 7 ft by 7√2 ft, or approximately 23.9 feet, or 7.97 yd

and ...

The area of the triangular shape is A = (1/2)(base)(height), which here is

A = (1/2)(7)(7) = 49/2 ft^2, or 16.4 yd^2

x = 27

Step-by-step explanation:

Use the ratio and proportion:

  10   =     14    

x + 8     2x - 5

just X multiply:

14 ( x + 8 ) = 10 ( 2x - 5 )

-6x = -162

x = -162 / -6

x = 27