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The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right angle. Yes. No.

Sagot :

Dead3illidn

Answer:

Yes

Step-by-step explanation:

3 , 4 & 5 are Pythagorean Triplet numbers. When lengths of a triangle's 3 sides are Pythagorean Triplet , the triangle is a right angled triangle.

The triangle will be a right angled triangle only when the hypotenuse will have length of 5 and other 2 sides will have length of either 3 or 4.

Sarah06109idn

Answer:

[tex]\boxed {\boxed {\sf Yes, \ the \ side \ lengths \ 3, \ 4, \ and \ 5\ can \ make \ a \ right \ triangle}}[/tex]

Step-by-step explanation:

If the triangle is a right triangle, then the sides will check out in the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

Where a and b are the legs and c is the hypotenuse.

1. Define Sides

The legs are the 2 shorter sides and the hypotenuse is the longest.

The sides given are 3, 4 (shorter), and 5 (longest). Therefore:

[tex]a=3 \\b=4 \\c=5[/tex]

2. Check the Sides in the Theorem

Substitute the values into the theorem.

[tex](3)^2+(4)^2=(5)^2[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction.

Solve all of the exponents first.

  • (3)² = 3*3= 9
  • (4)²= 4*4= 16

[tex]9+16=(5)^2[/tex]

  • (5)²= 5*5= 25

[tex]9+16=25[/tex]

Add the numbers on the left side of the equation.

[tex]25=25[/tex]

This is true. 25 is equal to 25, so this triangle can be a right triangle.

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