Question

50 points plsssss help

12. A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain.

Answer 1

`\boxed{\textsf{ \textbf{ Yes} , the given triangle is a right angled triangle .}}`

Explanation:

We are given three sides of the triangle and we need to say that whether the triangle is right Angled triangle or not . The given side lenghts are 6 cm , 8 cm and 10 cm . ( Units not given in Question ) .

`\textsf{$\implies$ Sides = 6cm , 8cm and 10 cm .}`

So , a triangle with its given sides will be a right angled triangle if it has a right angle . And the sum of squares of two smallest sides must be equal to the square of the longest side . ( According to Pythagoras Theorem ) .

Here two smallest sides are 8cm and 6cm .

`\implies\textsf{ $\sf Sides_((smallest))$= 8cm and 6 cm }`

And the largest side is 10 cm .

`\sf\implies Side_((largest))= 10 cm`

And here the sum of squares of 8cm and 6cm should be equal to the square of 10cm in order to Prove it a right angled triangle .

`\sf\implies (8cm)^2+(6cm)^2 = (10cm)^2 \\\\\sf\implies 64 cm^2+36cm^2 = 100 cm^2 \\\\\sf\implies \boxed{\pink{\frak{ 100 cm^2=100cm^2}}}`

Since LHS = RHS hence the triangle is a right angled triangle .

Figure :-

`\setlength{\unitlength}{1 cm}\begin{picture}(12,8)\thicklines \put(0,0){\line(1,0){4.49}}\put(0,0.01){\line(0,1){3}}\put(0,3){\line(3,-2){4.44}}\put(4.9,-0.3){\sf C }\put(0,-0.3){\sf B }\put(0,3.3){\sf A}\put(2,-0.5){\sf 8\: cm }\put(-1,1.5){\sf 6\: cm }\put(2,2){\sf 10\: cm }\put(0.2,0){\line(0,1){0.2}}\put(0.2,0.2){\line(-1,0){0.2}}\end{picture}`

Answer 2

yes, it is a right triangle

Explanation:

• remember: a triangle can only be a right triangle if it works with the pythagorean theorem
• therefore, we can plug in the numbers we have in the formula
• know the formula: a^2 + b^2 = c^2
• now, plug in

a^2 + b^2 = c^2

6^2 + 8^2 = 10^2

• the largest side is always the hypotenuse
• we have to see if both sides equal to the same value

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

• yes they are equal, therefore it is a right triangle