Question

A triangle has sides with lengths of 12 miles, 84 miles, and 85 miles. Is it a right triangle?

Answer 1

Answer:

$\boxed {\boxed {\sf No}}$

Step-by-step explanation:

If a triangle is a right triangle, it can satisfy Pythagorean Theorem.

$a^2+b^2=c^2$

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

12 and 84 are the legs because are they shortest. 85 is the hypotenuse because it is the longest side.

$a= 12 \\b=84 \\c=85$

Substitute the values into the formula.

$(12)^2+(84)^2=(85)^2$

Solve the exponents.

• 12²= 12*12=144
• 84²=84*84=7056
• 85²= 85*85=7225

$144+7056=7225$

Add on the right side.

$7200\neq 7225$

7220 is not equal to 7225, so these sides cannot be a right triangle.

Answer 2

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