We know, equation of ellipse is given by :
Here,
(h,k) is centre of the ellipse = (0,0).
a = major axis = 8.
b = minor axis = 4.
Putting all given value in above equation, we get :
Hence, this is the required solution.
Answer in fraction form: x = 55/4
Answer in decimal form: x = 13.75
Both forms are equivalent, but they say it in a slightly different way.
===========================================================
Work Shown:
AC/QY = CD/YW
(x+5)/15 = 5/4
4(x+5) = 15*5
4x+20 = 75
4x = 75-20
4x = 55
x = 55/4
x = 13.75
------------
Explanations:
- The first step is possible because the polygons are similar. Similar figures have their corresponding sides be in the same proportion or ratio. Note how side AC has the double red angle (at point A) and a single red angle (point C). The side QY has the same idea in the same order. This is why AC corresponds to QY. The ratio AC/QY is the same as CD/YW.
- In the second step, I plugged in the expressions that the diagram shows. This is the substitution property.
- On step 3, I cross multiplied. The general format is A/B = C/D cross multiplies to A*D = B*C.
From the facts given, the swimming pool and the floor of the gym has the same in size. The pool has a dimension of 75 ft by 60 ft. Basically, the possible size of the gym floor is also 75 ft by 60 ft.
