SOLUTION: A 3D figure has a right triangular base. The perimeter of the base is 5 linear yards. The area of the base is 1 1/8 yards squared. The volume of the figure is 5 1/16 yards cubed. T

Algebra ->  Triangles -> SOLUTION: A 3D figure has a right triangular base. The perimeter of the base is 5 linear yards. The area of the base is 1 1/8 yards squared. The volume of the figure is 5 1/16 yards cubed. T      Log On


   

Question 865703: A 3D figure has a right triangular base. The perimeter of the base is 5 linear yards. The area of the base is 1 1/8 yards squared. The volume of the figure is 5 1/16 yards cubed. The height of the figure is 3 times the length of the height of the base. What are the dimensions of the figures base? What is the height of the figure?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A 3D figure has a right triangular base. The perimeter of the base is 5 linear yards.
The area of the base is 1 1/8 yards squared.
The volume of the figure is 5 1/16 yards cubed.
The height of the figure is 3 times the length of the base.
What are the dimensions of the figures base?
:
Change to improper fractions
9/8 sq/yds area
81/16 cu/yds volume
:
What is the height of the figure?
the height of the figure equals the vol divided by the area of the base
81%2F16 divided by 9%2F8
81%2F16*8%2F9 = 9%2F2 = 41%2F2 yds high
:
base = 1/3 the height
9%2F2 * 1%2F3 = 3%2F2 = 11%2F2 yds side of the base
Find the other side (s)of a right triangle using the Area of the triangle
1%2F2*3%2F2*s = 9%2F8
use decimals here
.5 * 1.5 * s = 1.125
.75s = 1.125
s = 1.125/.75
s = 1.5 yds for the 2nd side too
Find the 3rd side of the triangular base, which has a perimeter of 5
1.5+1.5+s = 5
s = 5-3
s = 2
The base is 1.5 by 1.5 by 2
;
:
Check this by finding the volume
.5*1.5*1.5*4.5 = 5.0625 which is 5 1/16 cu/yds