SOLUTION: Two similar triangles have sides in the ratio of 4:5. What is the ratio of their perimeters? A regular square pyramid has a base with edges 16 and height 15. What is the volume

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Question 38602This question is from textbook
: Two similar triangles have sides in the ratio of 4:5. What is the ratio of their perimeters?
A regular square pyramid has a base with edges 16 and height 15. What is the volume and surface area of the pyramid? This question is from textbook

Answer by venugopalramana(3286) About Me  (Show Source):
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Two similar triangles have sides in the ratio of 4:5. What is the ratio of their perimeters?
LET THE SIDES BE 4X,4Y,4Z AND 5X,5Y,5Z
PERIMETER RATIO=4(X+Y+Z)/5(X+Y+Z)=4/5
A regular square pyramid has a base with edges 16 and height 15. What is the volume and surface area of the pyramid?
VOLUME =BASE AREA*HEIGHT/3=16*16*15/3=1280
LET ABCD BE THE SQUARE BASE AND T BE THE VERTEX.THE ALTITUDE TS FROM TOP TO BASE WILL MEET THE BASE AT S THE POINT OF INTERSECTION OF DIAGONALS AC AND BD.
LET MIDPOINT OF AB BE P.THEN PT IS THE SLANT HEIGHT
IN RIGHT TRIANGLE PST,WE HAVE
PT^2=PS^2+ST^2=8^2+15^2=64+225=289
PT=17
HENCE AREA OF ONE SLANT SURFACE ABT=0.5*16*17=136
TOTAL SLANT AREA=4*136=544