Question

Can anyone help me with this problem ? I would appreciate it a lot !

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Find the area of the triangle

Answer 1

D - 192

Explanation:

So the solve this, lets use the formula for area of a triangle:

b*h / 2 = A

b is the base, h is the height.

In this case, our base is 32, and our height is unknown.

To find it we must use pythagreons theorm:

`a^2+b^2=C^2`

a is half of the base in this case, since tecnically this iscoceles traingle(2 same sides) cut in half is 2 right triangles.

32/2 = 16

b is the unknown, and C is the hypotenuse(longest length) which is 20:

`16^2+b^2=20^2`

`256*b^2=400`

`b^2=144`

`b=12`

So we know b, whihc is our height, is 12.

Plugging this in:

32*12 / 2 = A

384 / 2 = A

192 = A

So the area of the triangle is 192.

Hope this helps!

Answer 2

D: 192 square ft

Explanation:

We are given all 3 side lengths of the triangle, and we notice that 2 of the sides are congruent (the 2 sides that are 20 ft). Therefore, we can safley say that this triangle is isosceles. What this tells us is that the height bisects the base. This is important because we can say that the base for each of the right triangles created by the height is 16. From there, we can say that h = 12 because 20 and 16 are basically 4 and 5 multiplied by 4, which means that the side lengths form a scaled-up version of the Pythagorean Triple 3-4-5. Now, just calculate the area by doing
`(1)/(2)*32*12` (basically just half * base * height), which gives us 192
`ft^(2)`. Hope this helps! Feel free to reach out if you have any further questions.