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1 answer:
Answer:
1. a. 25 in²
2. NO. The side lengths don't form a triangle, so cannot form a right triangle.
3. 17
4. 9
Step-by-step explanation:
These are exercises in the application of the Pythagorean theorem, which tells you that for a right triangle, the square of the hypotenuse is the sum of the squares of the other two sides.
In every case, you are given two sides and asked to find the third. Based on the given sides, you need to determine whether you're finding a sum (the hypotenuse) or a difference (one leg).
Since the theorem gives the relation between the squares, you need to find the square root of the sum or difference in order to find the actual length.
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In the first problem, the squares are shown as actual squares, the area of which is equal to the square of the side length. The Pythagorean theorem tells you the larger square has an area that is the sum of the areas of the smaller squares.
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We can find m∠BCD like follows: m∠BCD=90°-45°=45<span>°
Now, m</span><span>∠DBC= 180°-(90°+45°)=45°
Remember that </span>
, so 
We know that hypotenuse= BC= 3in and
=∠DBC)=45°, so replacing the values we get:
We can conclude that the segment CD is 2.12 in
Now, m</span><span>∠DBC= 180°-(90°+45°)=45°
Remember that </span>
We know that hypotenuse= BC= 3in and
We can conclude that the segment CD is 2.12 in