Question 1016790: a patio is configured from a rectangle with two right triangles of equal size attached at the two ends.The length of the rectangle is 38 ft. The base of the right triangle is 4 ft less than the height of the triangle. If the total area of the patio is 1155 ft^2 determine the base and height of the triangular portions
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a patio is configured from a rectangle with two right triangles of equal size attached at the two ends.
The length of the rectangle is 38 ft.
The base of the right triangle is 4 ft less than the height of the triangle.
If the total area of the patio is 1155 ft^2 determine the base and height of the triangular portions
:
The way I see this, the height of the right triangle is also the width of the rectangle.
h = the height of the triangle and the width of the rectangle
(h-4) = base of the triangle
:
The two right triangles form a rectangle whose area is h(h-4)
:
An equivalent rectangle is formed with length of (h-4) + 38 = (h+34); width = h
Total area
h(h+34) = 1155
h^2 + 34h - 1155 = 0; a quadratic equation; a=1; b=34; c=-1155
Using the quadratic formula, the positive solution
h = 21 ft is the height of the triangle
and
21-4 = 17 ft is the base of the triangle
:
:
Check this, find the area of the rectangular section and the 2 triangles
38 * 21 = 798 sq/ft
17 * 21 = 357
--------------
total area: 1155
|
|
|
