In 16 by 12 rectangle , what is the perimeter of the triangle formed by two sides of the rectangle and the diagonal.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The rectangle has sides with a length 16 and 12. The length of the diagonal of a rectangle with sides a and b is given by sqrt(a^2 + b^2).

Substituting the values given , the length of the diagonal is sqrt(16^2 + 12^2)

=> sqrt (256 + 144)

=> sqrt 400

=> 20

The perimeter of the triangle made with the sides and the diagonal is 20 + 12 + 16 = 48

The perimeter of the triangle is 48.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Let the length be L= 16 and the width be w = 12.

Since the sides of a rectangle are perpendicular to each other, the triangle formed by two sides of rectangle and the diagonal is a right angle triangle.

The hypotenuse of the right angle triangle is the diagonal of rectangle and the legs are the length and the width of rectangle.

Let D be the diagonal of rectangle and the hypotenuse of right angle triangle.

To calculate the perimeter of this triangle, we need to know all the lengths of the sides, but, for the moment, we only know the lengths of the legs.

We'll determine the length of hypotenuse using the Pythagorean theorem:

D^2 = L^2 + w^2

D^2 = 16^2 + 12^4

D^2 = 256 + 144

D^2 = 400

D = 20

Since the length of a side cannot be negative, we'll keep only the positive value of D.

We can calculate now the perimeter of triangle:

P = L + D + w

P = 16 + 20 + 12

P = 48

The requested perimeter of triangle formed by two sides of rectangle and the diagonal of rectangle is  p  = 48 units.

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