Indicate whether the figures described below are always, sometimes or never geom
ID: 3120422 • Letter: I
Question
Indicate whether the figures described below are always, sometimes or never geometrically similar Two Squares always isosceles triangles. sometimes Two equilateral triangles always Two pentagons Sometimes Two regular pentagons. always Two rectangles Sometimes A square and a rectangle. Sometimes Two circles always A regular pentagon and a regular hexagon. never Two angles sometimes A mature gorilla weighs 400 pounds and stands 5 feet tall Give an estimate of its weight when it was half as tall. 50 pounds What assumptions are involved in your estimate. When half as tall, geometrically similar A mature gorilla's two feet together have a combined area of about 1 square foot When the gorilla is standing on its feet, what is the pressure on its feet, in pounds per square inch? 400 pounds per square foot = 400/12^2 = 2.78 lb/in^2 Suppose King Kong is a gorilla scaled up with a scaling factor of 10 How much does King Kong weigh? 400,000 pounds What is the pressure on the King's feet, in pounds per square inch? 400,000 lb/10^2 ft^2 = 4000 lb/12^2 in^2 = 27.78 lb/in^2 The movie THEM features enormous ants (about 8m long and about 3m wide). We can investigate how feasible such a scaled-up insect is by considering its consumption. A common ant, which is about 1 cm. long, needs about 24 milliliters of oxygen per second for each cubic centimeter of its volume. Since an ant does not have lungs, it must absorb the oxygen through its "skin which it can do at a rate of about 6.2 milliliters per second per square centimeter. We may suppose that the tissues of the scaled-up ant would have the same need for oxygen for each cubic centimeter of body and that its skin could absorb oxygen at the same rate as a normal ant. Compared to a normal ant, how many times as large is an enormous ant's length? 800 surface area? 800^2 volume? 800^3 what proportion of such an ant's oxygen need could its skin supply? Supply/need = 800^2/800^3 = .00125 or .125% what can you conclude about the existence of such insects? Could not exist A six foot indoor holiday tree needs four strings of lights to decorate it. How many strings of lights will be needed for an outdoor tree that is 30 feet high? 4 (5^2) = 100 stringsExplanation / Answer
Q1.a.Two squares are similar because all angles of one square equales all angles of other square,each 90.Also corresponding sides of two squares are proportional.
B.In an isosceles triangle two sides and angles opposite to these sides are equal.But in two isosceles triangles they may be different.
C.Two equilateral triangles are always similar,because each angle is 60 and all sides are equal.So corresponding angles of two equilateral triangles are equal and sides are proportional.
D.Two pentagons may be similar or not.because all angles may be different and sides also.
E.Regular pentagons are similar because all angles are equal and similarly all sides.
F.Two rectangles have only two angles equal and these could be different in two different rectangles.
G.A square is also a rectangle.so sometimes may be similar sometimes not.
H.Two circles are always same as they are in same shape.
I.regular Pentagon has different angles than regular hexagon.and sides are also different.
J.Two angles are similar if equal,if not equal then not similar.
Q2.a.weight of gurrela when it was 5 feet=400ponds.
Weight per feet=20 ponds.
Therefore,weight of gurrela when it was half its height=20(5/2)=50ponds.