Answer:
17150 ft²
Step-by-step explanation:
similar rectangles means that the scaling factor from one rectangle to the other is the same for every side. and so the relative ratio of length and width stays the same.
in our case now the 2 widths are 175 feet and 40 feet.
the scaling factor f from small to large is therefore 175/40 = 35/8.
width large = width small × f
length large = length small × f
the area of a rectangle is length × width.
we know the area of the small rectangle (896 ft²).
Asmall = 896 = length small × width small
now the area A of the large rectangle is
A = length large × width large =
= length small × f × width small × f =
= length small × width small × f² = Asmall × f² =
= 896 × (35/8)² = 17150 ft²
