SOLUTION: A triangle had the following side lengths: 33 ft, 56 ft and 65 ft. Was it a right triangle? Explain.

Question 101989: A triangle had the following side lengths: 33 ft, 56 ft and 65 ft. Was it a right triangle?
Explain.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If this is a right triangle, then the Pythagorean theorem applies. The Pythagorean theorem says
that in a right triangle the square of the length of the hypotenuse (the longest side) equals
the sum of the squares of the two remaining sides (called the legs). So if the triangle
is a right triangle the square of the longest side (65 ft) equals the sum of the square of the
shortest side (33 ft) plus the square to the remaining side (56 ft). In equation form this
becomes:
.

.
If this equation is true, then the triangle is a right triangle.
.
On the left side the square of 65 is 65 times 65 which is 4225. On the right side the
square of 33 is 33 times 33 which is 1089 and the square of 56 is 56 times 56 which is 3136.
.
Substituting these values into the Pythagorean base equation results in:
.

.
and adding the two numbers on the right side leads to the equation becoming:
.

.
Since the Pythagorean equation is true for this triangle, the triangle is a right triangle.
.
Hope this helps you to understand how you can do this problem.
.

RELATED QUESTIONS
A triangle had the following side lengths: 33 ft, 56 ft and 65 ft. Was it a right... (answered by MathLover1)

Consider a triangle with side lengths of 10 ft, 17.32 ft, and 20 ft. By examining the... (answered by MathLover1,ikleyn)

In a triangle the lengths of the sides are 5 ft, 11 ft, and 13 ft. Is this a right... (answered by sachi)

A right triangle has a hypotenuse of length c = 65 ft. Use the Pythagorean Theorem to... (answered by solver91311)

Is it possible to construct a triangle with side lengths of 1 ft, 3 ft, and 4 ft? Why or... (answered by Alan3354)

the lengths of three sides of a triangle are given.determine whether each triangle is a... (answered by Alan3354)

A triangle has sides with lengths of 33�centimeters, 56�centimeters, and 65�centimeters.... (answered by rothauserc)

A triangle has side lengths 12 ft, 13 ft, and 14 ft. Find the measure of the angle... (answered by J2R2R)

Determine whether each triangle with sides of given lengths is a right angle Problem= (answered by mananth)