Answer:
Part A) The triangles ABC and EDC are similar by AAA, because the three internal angles are equal in both triangles
Part B) The width of the river is about
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
Part A) we know that
In this problem , triangles ABC and CDE are similar by AAA, because its corresponding angles are congruent
so
m<DCE=m<ACB -----> by vertical angles
m<EDC=m<ABC -----> is a right angle
m<DEC=m<CAB -----> the sum of the internal angles must be equal to 180 degrees
Part B) we know that
The triangles ABC and EDC are similar -------> see Part A
therefore
substitute the values and solve for AB
To answer the question above, I let x be the number of calendars sold. You may use any other letter as this is just for representation. The total income generated in selling calendars is calculated by multiplying the number of calendars with the price. That is,
total income = 5x
If we let total income be y, our equation is further simplified into,
y = 5x
Because
and
are inversely proportional, there is some constant
such that
Given that
and
, we have
So when
, you have
W= width
l= length= 4w
Area= lw
16 square yards= lw
substitute l=4w for l
16= (4w)(w)
16= 4w^2
divide both sides by 4
4= w^2
take the square root of 4
2 yards= w
LENGTH
l=4w
l=4(2)
l=8 yards
CHECK:
16= (8)(2)
16= 16
ANSWER: The length is 8 yards and the width is 2 yards.
Hope this helps! :)