Answer:
Area of the smaller triangle 74 ft².
Step-by-step explanation:
Given : The triangles are similar. The area of the larger triangle is 206 ft^2.
To find : Find the area of the smaller triangle to the nearest whole number.
Solution : We have given that triangles are similar and area of the larger triangle is 206 ft^2.
By the similar triangles property : [tex]\frac{Area\ of\ triangle 1}{Area\ of\ triangle\ 2} = \frac{(side\ of\ triangle\ 1)^{2}}{(side\ of\ triangle\ 2)^{2} }[/tex].
Then Side of triangle 1 = 15 ft .
Side of triangle 2 = 9 ft.
Area of triangle 1 = 206 ft².
Let area of triangle 2 = x.
Then ,
Ratio of sides = [tex]\frac{15}{9}[/tex] = [tex]\frac{5}{3}[/tex]
[tex]\frac{206}{x} = \frac{(5)^{2}}{(3)^{2} }[/tex].
[tex]\frac{206}{x} = \frac{(25}{9}[/tex].
On cross multiplication :
206 * 9 = 25 *x
1854 = 25 * x .
On dividing by 25
x = 74.16 ft².
Therefore, Area of the smaller triangle 74 ft².
