A juice container is a square prism with base edge length 4 inches. When an 8-inch straw is inserted into the container as shown
, exactly 1 inch remains outside the container. The length of AB is ___ inches, to the nearest inch. (Enter only the number.)
1 answer:
Assuming AB is the height because we are given it has a square base with 4 by 4
so draw a diagram ( see attachment)
given tha the 8 inch straw ha 1 inch sticking out, the diagonal is 7
use pythagorean theorem twice since 2 right triangles
a^2+b^2=c^2
4^2+4^2=c^2
16+16=c^2
32=c^2
sqrt both sides
4√2=c
the bottom diagonal is 4√2
bottom^2+height^2=7^2
(4√2)^2+(AB)^2=7^2
32+(AB)^2=47
minus 32 both sides
(AB)^2=15
sqrt both sides
AB=√15
if AB is the height
so draw a diagram ( see attachment)
given tha the 8 inch straw ha 1 inch sticking out, the diagonal is 7
use pythagorean theorem twice since 2 right triangles
a^2+b^2=c^2
4^2+4^2=c^2
16+16=c^2
32=c^2
sqrt both sides
4√2=c
the bottom diagonal is 4√2
bottom^2+height^2=7^2
(4√2)^2+(AB)^2=7^2
32+(AB)^2=47
minus 32 both sides
(AB)^2=15
sqrt both sides
AB=√15
if AB is the height
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