is it possible to construct a triangle with the given side lengths 28, 17 and 46 units if not explain why not
1 answer:
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Answer:
33.75 cubic inches of styrofoam can be placed inside the container.
Step-by-step explanation:
Based on given information, the volume of the prism (), in cubic inches, is determined by using this formula:
(1)
Where:
- Base of the triangular face, in inches.
- Height of the triangular face, in inches.
- Length of the prism, in inches.
If we know that ,
and
, then the volume of the prism is:
33.75 cubic inches of styrofoam can be placed inside the container.
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Check Attachment!!!
According to the statement of the question, we have:
a/b = 3/4
<em>Note that according to the attached figure, </em><em>b > a</em><em>, then the correct proportion will be </em><em>a</em><em> to </em><em>3</em><em>, as well as </em><em>b</em><em> to </em><em>4</em><em>, because </em><em>b > a</em><em> and </em><em>4 > 3</em>
Isolating a and b:
a = 3b/4
b = 4a/3
From Pythagoras:
h² = a² + b² - as a = 3b/4 and b = 4a/3, so
<h3>b = 4h/5</h3><h3>a = 6h/5</h3>For Area:
A = b.a/2
as b = 4h/5 and a = 6h/5, so
<h3>A = 12h/25</h3>