Tplokingeridn
Answered

IDNLearn.com offers a user-friendly platform for finding and sharing answers. Ask any question and receive accurate, in-depth responses from our dedicated team of experts.

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.

We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.