To solve: Given statement is: The lengts of the sides of a right triangle are consecutive multiples of 3.Find the length of the hypotenuse.

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To solve: Given statement is:  The lengts of the sides of a right triangle are consecutive multiples of 3.Find the length of the hypotenuse.

coffentw · Accepted Answer

Calculation:  Let a= length of one side  a+3= length of the other side  a+6= length of the hypotenuse [since the hypotenuse is the longest side]  The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the sides of the right angles triangle.  So,  a2+(a+3)2=(a+6)2  ⇒a2+a2+2⋅a⋅3+9=a2+2⋅a⋅6+36…..[(x+y)2=x2+2xy+y2]  ⇒2a2+6a+9=a2+12a+36  ⇒2a2−a2+6a−12a+9−36  =0...........[subtract (a2+12a+36) from each side]  ⇒a2−6a−27=0  ⇒a2−9a+3a−27  =0...........  [factor the middle term such that the sum of the factor is equal to the middle term and product of the factors is equal to the product of the first and the last term.]  ⇒a(a−9)+3(a−9)=0  ⇒(a+3)(a−9)=0  ⇒a+3=0 or a−9=0…….[ab=0⇔a=0orb=0]  ⇒a=−3ora=9  Since a is the length of the triangle, it cannot be negative.  So, a=9 units  a+3=12 units  a+6=15 units  So, the hypotenuse is 15 units.

To solve: Given statement is: The lengts of the sides of

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