Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1st picture: b. 12, 16, 20
2nd picture: b. 14

3rd picture: b. 20,21,29

Explanation:

For 1st Picture:

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Longest side is hypotenuse.

let's check a. 5, 12 , 14

14^2=5^2+12^2

196≠169

Not right angled triangle

let's check b. 12, 16, 20

20^2=12^2+16^2

400=400

It's a right angled triangle

therefore, answer is b. b. 12, 16, 20

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For 2nd pictiure:
Given:

Opposite =RG= 17

Hypotenuse= TG=22

base= RT=?

Approach:

• We can use the Pythagorean theorem to solve for the length of the base.

• The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Solution:

Let x be the length of the base.

Applying the Pythagorean theorem, we get:

TG^2 = RG^2 + RT^2

22^2 = 17^2 + RT^2

RT^2=22^2-17^2

RT=\sqrt{195}

RT= 14

so, the answer is b. 14

`\hrulefill`

For 3rd picture:

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Longest side is hypotenuse.

let's check a. 8,10,17

17^2=8^2+10^2

289≠164

Not right angled triangle

let's check b. 20,21,29

29^2=20^2+21^2

841=841

Since it is a right angled triangle.

Therefore, answer is b. 20,21,29