Need : ) only 100% answers 1) an egyptian pyramid has a square base that measures 80 meters on each side. if the height of the pyramid is 30 meters, what is the slant height of the pyramid? 2) a room in a bank is shaped like the rectangular prism shown below. the room has a security system that is triggered by two laser beams which stretch from point a to d and point b to c. how many total feet of laser beams are there? *a 3-d rectangle 15 ft. length the back rectangle 12 ft. width the side 35 ft. width front*

1)  the slant height of the pyramid is 50 meters.

2) there are (approximately) a total of 80 ft of laser beams.

Step-by-step explanation:

1) The height of the pyramid (30 m) and half of the length of its base (40 m) form a rectangular triangle, where the slant height is its hypotenuse (H). From Pythagorean theorem:

H^2 = 30^2 + 40^2

H = √2500

H = 50 m

2) In the figure attached the rectangular prism is shown (point E was added).

The length of the laser beams is the addition of the segments AD to segment CB (which are equal).

We can make a rectangular triangle between points ECD. From Pythagorean theorem:

ED^2 = EC^2 + CD^2

ED = √(12^2 + 35^2)

ED = 37 ft

We can make a rectangular triangle between points AED. From Pythagorean theorem:

AD^2 = EA^2 + ED^2

AD = √(15^2 + 37^2)

AD ≈ 40

Then, there are (approximately) a total of 80 ft of laser beams.

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