Answer:
about 252.78 ft
Step-by-step explanation:
Define angle QMP as α. Then ...
MN = 60·sin(α)
NP = 60·cos(α)
area MPN = (1/2)(MN)(NP) = 1800sin(α)cos(α)
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PQ = 60tan(α)
area MPQ = (1/2)(MP)(PQ) = 1800tan(α)
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The ratio of areas is 2.5, so we have ...
1800tan(α) = 2.5·1800sin(α)cos(α)
1 = 2.5cos(α)² . . . . . . divide by 1800tan(α)
cos(α) = √0.4 . . . . . . solve for cos(α)
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Then the perimeter is ...
Perimeter = MN +NP +PQ +QM = 60sin(α) +60cos(α) +60tan(α) +60/cos(α)
= 60(sin(α) +cos(α) +tan(α) +sec(α))
= 60(0.774597 +0.632456 +1.224745 +1.581139)
= 60(4.212936) = 252.776
The perimeter of the trapezoid is about 252.776 feet.
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With perhaps a little more trouble, you can find the exact value to be ...
perimeter = (6√10)(7+√6+√15)
The height (h) of the rectangular prism is: 1.9 feet.
<h3>How to Find the Volume of a Rectangular Prism?</h3>
A rectangular prism has a length (l), height (h), and a width (w). The volume of the rectangular prism is calculated using the formula given as: V = (length)(width)(height).
Given the following parameters:
Volume of the rectangular prism = 30.45 ft^3,
Length (l) = 6.3 ft,
Width (w) = 2.5 ft.
Height of the rectangular prism (h) = ?
Plug in the values
(6.3)(2.5)(h) = 30.45
15.75h = 30.45
15.75h/15.75 = 30.45/15.75
h ≈ 1.9 ft
Learn more about volume of rectangular prism on:
brainly.com/question/12917973
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From the diagram,
Angle
Bisecting an angle means dividing the angle into two equal part.
1/2 m
Either 7x or -3x hope this helps hun!!
The factors of 45 are:
1, 3, 5, 9, 15, 45Which numbers multiply together to equal 45?
