The area of smaller triangle is 59 square feet
What are the similar triangles?
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
What is the formula for the area of triangle?
The formula for the area of triangle is
[tex]Area = \frac{1}{2} \times base \times \ height[/tex]
According to the given question.
The area of the larger triangle is 105 square feet.
And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.
Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.
Since, the corresponding edges of similar triangles are proportional.
Therefore,
[tex]\frac{y}{x} = \frac{16}{12}[/tex]
[tex]\implies y = \frac{4}{3} x[/tex]
Also, the area of larger triangle is 105 square feet.
[tex]\implies \frac{1}{2} \times \frac{4}{3} x \times 16 = 105[/tex]
The above euqtaion can be written as
[tex]\implies \frac{1}{2}\times \frac{4}{3} x \times \frac{4}{3} \times 12 = 105[/tex]
[tex]\implies \frac{1}{2} \times (\frac{4}{3} )^{2} \times x \times 12 = 105[/tex]
[tex]\implies \frac{1}{2} \times x \times 12 = 105 \times \frac{9}{16}[/tex]
[tex]\implies \frac{1}{2} \times x \times 12 = 59[/tex]
⇒ Area of smaller triangle = 59 square feet
Hence, the area of smaller triangle is 59 square feet.
Find out more information about area of triangle and similar triangles here:
https://brainly.com/question/16394875
#SPJ2
