Which set of side lengths is a pythagorean triple? 2, 3, 13 5, 7, 12 10, 24, 29 11, 60, 61

The correct answer is "11,60 and 61".

Step-by-step explanation:

The expression from the Pythagoras theorem in the right triangle is as follows;

                     ...... (1)

Here, AC is the longest side which is hypotenuse, AB is the shortest side which is perpendicular in the right triangle and BC is the side of the triangle.

Only 11, 60 and 61 satisfies the above expression.

Therefore, L.H.S is equal to R.H.S. It satisfies the Pythagoras theorem.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2