1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jeka94
3 years ago
5

a triangular prism has an isosceles right triangular base with a hypotenuse of square root of 32 and a prism height of 12. a squ

are prism has a height of 12 and its volume is equal to that of the rectangular prism. what are the dimensions of the square base, in simplest radical form?
Mathematics
1 answer:
omeli [17]3 years ago
3 0

Answer:

The lengths of the sides of the square base are  2\sqrt{2}\ units

Step-by-step explanation:

<u><em>The correct question is</em></u>

A triangular prism has an isosceles right triangular base with a hypotenuse of square root of 32 and a prism height of 12. a square prism has a height of 12 and its volume is equal to that of the <em><u>triangular</u></em> prism. what are the dimensions of the square base, in simplest radical form?

we know that

The volume of a prism is given by the formula

V=Bh

where

B is the area of the base

h is the height of the prism

so

If the volumes of the solids are the same and their  heights are the same, then the area of the base of the triangular prism must be equal to the area of the base of the square prism

step 1

Find the area of the base of the triangular prism

Remember that in a right isosceles triangle, the two legs are equal

Let

x ---> the length side of each leg

Applying the Pythagorean Theorem

(\sqrt{32})^2 =2x^2

x^2=32/2\\x^2=16\\x=4\ units

The area of the triangular base is equal to

A=\frac{1}{2}(4)(4)=8\ units^2

step 2

Find the dimensions of base of the square prism

Let

b ---> the length side of the square base

The area of a square is given by the formula

A=b^2

we have

A=8\ unit^2 ----> is the same that the area of triangle

substitute

8=b^2

b=2\sqrt{2}\ units

therefore

The lengths of the sides of the square base are  2\sqrt{2}\ units

You might be interested in
NEED HELP ASAP What is true about the points on the graph of Y=3^x?
galben [10]

Answer:

d

Step-by-step explanation:

The answe of this question is d

3 0
3 years ago
What is the missing term in the factorization?
ludmilkaskok [199]
3(2x+5)(2x-5), 5 is the missing term.

8 0
3 years ago
Read 2 more answers
Can you help me with this question?
Rufina [12.5K]

Answer:

  16.2

Step-by-step explanation:

The angle internal to the triangle at B is the supplement of the one shown, so is 65°. That is equal to the angle internal to the triangle at D. Since the vertical angles at C are congruent, the two triangles are similar by the AA theorem.

Corresponding sides of similar triangles are proportional, so we can write the proportion shown in the attachment:

  BC/FC = DC/AC

  BC = FC(DC/AC) = 21.6(7.2/9.6)

  BC = 16.2 . . . . matches the first choice

4 0
3 years ago
What is 7.13×10 to the fifth power in standard form
horrorfan [7]
713000 is your answer
4 0
3 years ago
Pleaseeee helppp i’m running out of time
PilotLPTM [1.2K]

Answer:

Square Root of 162 ~ 12.727

Step-by-step explanation:

Simply do the Pythagorean Theorem!

a^2 + b^2 = c^2

This case we're solving for the long side which is the hypothenuse.

9^2+9^2= c^

81+81=c^

162=c^

Square root of 162

Which is 12.727

3 0
2 years ago
Other questions:
  • Han ran 10 meters in 2.7 seconds.Priya ran 10 meters in 2.4 seconds.Who is faster?
    11·2 answers
  • Value of 6n-2 when n=3
    6·2 answers
  • Mr. Vazquez determines that the area of a bathroom in his house is 25 square feet less than 1/5 of the area of the
    5·1 answer
  • Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =
    8·1 answer
  • Simplify 5^2•(4+2^3)
    6·1 answer
  • Please help me with this​
    5·1 answer
  • Two less than the product of nine is 12 more than the product of the number 3
    10·1 answer
  • Determine whether the function is periodic. If it is, find the period.
    12·1 answer
  • Do you guys know what -24/-6 =
    11·2 answers
  • What is the standard deviation from the mean <br> roundest to the nearest tenth
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!