Kevin has a triangle table cloth with side lengths of 5 inches,12 inches. He wants to cover a right angle triangle table cloth. Find if the cloth is appropriate for the
well, a common right triangle is 5-12-13
To determine if the triangle tablecloth is appropriate for covering a right-angle triangle table, we need to check if its side lengths satisfy the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the given side lengths of the tablecloth are 5 inches and 12 inches. We need to identify the longest side, which will correspond to the hypotenuse of the right-angled triangle.
So, we find the hypotenuse (c) by using the formula: c^2 = a^2 + b^2, where a and b are the lengths of the other two sides.
Let's plug in the values:
c^2 = 5^2 + 12^2
c^2 = 25 + 144
c^2 = 169
Now we can take the square root of both sides:
c = √169
c = 13
The length of the hypotenuse is 13 inches.
If the tablecloth's hypotenuse had been equal to the calculated value of 13 inches, it would have been appropriate to cover a right-angle triangle table. However, since the given tablecloth's hypotenuse length is 12 inches, which is less than 13 inches, it is not large enough to completely cover a right-angle triangle table.