Question

9. What formula could be used to find the area of the image?

10. Identify the dimensions that will be used in the formula in number 9.

11. What is the area of the image?

Answer 1

9. Area of triangle=
`(1)/(2) * base* height`

10. Base= 16 ft and Height= 15 ft.

11. 120 ft²

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=
`(16)/(2) = 8\ feet`

Now, finding the height of triangle by using pythagorean theorem.

We know,
`h^(2) = a^(2) +b^(2)`, where h is hypotenous, a is height or opposite and b is base or adjacent of triangle.

⇒
`17^(2)= a^(2) + 8^(2)`

⇒
`289= a^(2) + 64`

Subtracting both side by 64

⇒
`225= a^(2)`

taking square root on both side, remember; √a²=a

⇒a=
`√(225) = 15`

Hence, height of triangle is 15 ft.

Next, finding the area of triangle.

Formula; Area of triangle=
`(1)/(2) * base* height`

⇒ Area of triangle=
`(1)/(2) * 16* 15`

∴ Area of triangle= 120 ft²