Answer:
37.2
Step-by-step explanation:
when you turn the small triangle LMN to its right angle to cover the right angle of KLM, you find that they are similar triangles.
therefore the corresponding side lengths are at the same ratio.
LM/KM = MN/LN
LM = 24
MN = 13
we can get LN via Pythagoras of the small triangle
LN² + MN² = LM²
LN² + 13² = 24²
LN² = 24² - 13² = 576 - 169 = 407
LN = sqrt(407) = 20.174241
now back to our main problem
24/KM = 13/sqrt(407)
24×sqrt(407)/13 = KM = 37.2
The last one
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To find the volume of each prism, you will multiply the length by the width by the height.
V = lwh
3 3/4 x 3 x 3 1/4
V = 36 9/16 cubic feet
V = lwh
1/4 x 1/4 x 1/4
V= 1/64 cubic feet
Both boxes are similar in that they can be described as a rectangular prism.
They are different because one prism has congruent edges, so we call it a cube. The other one has varying side lengths, therefore it is only a rectangular prism.
Let the shortest side be = a, then side b = 2·a and side c = (b + 24)
We are given that a + b + c = 84
Substituting for b and c
a + 2·a + (a + 24) = 84
4·a + 24 = 84
4·a = 84 - 24 = 60
a = 60/4 = 15 feet
b = 2·15 = 30 feet
c = 15 + 24 = 39 feet
sorry if i am wrong