Answer:
9. Area of triangle= [tex]\frac{1}{2} \times base\times height[/tex]
10. Base= 16 ft and Height= 15 ft.
11. 120 ft²
Step-by-step explanation:
Given: Base of triangle= 16 ft
Length of leg of triangle= 17 ft.
As shown in the picture that median has bisected the triangle and forming two right angle triangle.
∴ Each base of right angle triangle= [tex]\frac{16}{2} = 8\ feet[/tex]
Now, finding the height of triangle by using pythagorean theorem.
We know, [tex]h^{2} = a^{2} +b^{2}[/tex], where h is hypotenous, a is height or opposite and b is base or adjacent of triangle.
⇒ [tex]17^{2}= a^{2} + 8^{2}[/tex]
⇒[tex]289= a^{2} + 64[/tex]
Subtracting both side by 64
⇒ [tex]225= a^{2}[/tex]
taking square root on both side, remember; √a²=a
⇒a= [tex]\sqrt{225} = 15[/tex]
Hence, height of triangle is 15 ft.
Next, finding the area of triangle.
Formula; Area of triangle= [tex]\frac{1}{2} \times base\times height[/tex]
⇒ Area of triangle= [tex]\frac{1}{2} \times 16\times 15[/tex]
∴ Area of triangle= 120 ft²
