The length of one leg of an isosceles right triangle is 3 ft . what is the perimeter of the triangle

Perimeter = 6+  ft

Step-by-step explanation:

Since given triangle is isosceles and right therefore two equals sides are the legs of right triangle given 3 and third side Hypotenuse say (x )  

Using Pythagorean theorem , we get  

taking square root both sides ,we get  

Three sides of given triangles are  

3 ft ,3ft and  

Perimeter is given by =   sum of  all three sides = 3+3+

                                                                              = 6 +   ft

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).