Answer:
rectangular is 114ft and triangular is 112ft
Step-by-step explanation:
Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT
Since VR = length * width and height
VR = 6*x*3
VR = 18x ft³
Also VT = Length *width * Height/2
VT = (7 * x * 4)/2
VT = 28x/2
VT = 14xft³
Since VR = 32 + VT
18x = 32+(14x)
collect like terms
18x-14x = 32
4x = 32
divide both sides by 4
4x/4 = 32/4
x = 8
Volume of the rectangular prism = 18x
Volume of the rectangular prism = 18*8
Volume of the rectangular prism = 144ft³
Volume of the right triangular prism = 14x
Volume of the rectangular prism = 14*8
Volume of the rectangular prism = 112ft³
The volume of the rectangular prism is 144 ft³ and the volume of the triangular prism is 112 ft³.
To find the volume of each figure, we'll use the formulas for volume of a rectangular prism and volume of a right triangular prism. The volume of a rectangular prism is given by the formula V = L × W × H, where L represents the length, W represents the width, and H represents the height.
The volume of a right triangular prism is given by the formula V = (1/2) × L × W × H, where L represents the length, W represents the width, and H represents the height.
Given the information provided, we have:
- For the rectangular prism: L = 6 ft, W = x (unknown), and H = 3 ft.
- For the triangular prism: L = 7 ft, W = x (unknown), and H = 4 ft.
We are also told that the volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism.
Let's set up the equations and solve for the volume of each figure:
Equation for the volume of the rectangular prism:
V_rectangular = L × W × H = 6 × x × 3 = 18x
Equation for the volume of the triangular prism:
V_triangular = (1/2) * L × W × H = (1/2) × 7 × x × 4 = 14x
We are given that the volume of the rectangular prism is 32 cubic feet more than the volume of the triangular prism. So, we can set up the equation: V_rectangular = V_triangular + 32
Substituting the equations for the volumes: 18x = 14x + 32
Simplifying the equation: 4x = 32
Dividing both sides by 4: x = 8
Now, we can find the volume of each figure by substituting the value of x:
Volume of the rectangular prism: V_rectangular = 18x = 18 × 8 = 144 ft³
Volume of the triangular prism: V_triangular = 14x = 14 × 8 = 112 ft³
Learn more about Prism here:
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Answer:
8.14
Step-by-step explanation:
Ok.So to do this, you have to know the Pytharomean Theroem.If you do not know how,then that is totally ok.I will tell.So the theroem has a formula.
Down below is a image showing the variables.
Now the hypotenuse is c.And b and a are the legs.
So we can put evaluses in the formula(formula:a^2 + b^2 = c):
(6.0)^2 + (5.5)^2 = c^2
36 + 30.25=c^2
66.25=c^2
8.14 = c
So 8.14 is the anwser!
Hoped it helped!
17.21 million without dicemal
Ans= 17,210,000
Answer:
Jaden has to plant the geranium in the circumcentre of the triangular yard in order such that it is equidistant from all its vertices.
Step-by-step explanation:
In Jaden’s yard, there is a triangular garden patch. He wants to plant a geranium in the patch at a point equidistant from all its vertices.
" The CIRCUMCENTER (C) of a triangle is the point in the plane equidistant from the three vertices of the triangle "
Hence Jaden has to plant the geranium in the circumcentre of the triangular yard in order such that it is equidistant from all its vertices.
Answer:
It’s b
Step-by-step explanation: