Question

A triangular corner is cut from a rectangular piece of paper and the resulting pentagon has 5,6,8,9,12 in some order.The ratio of the area of the pentagon to the area of the rectangle is
1) 11/18
2)13/18
3)15/18
4)17/18
This is a question of KVPY SA 2015.
Plz answer with correct explanation.
Best explanation will be marked Brainliest..

Answer 1

Answer:

Step-by-step explanation:

Since the pentagon is cut from a rectangle, the cut-off triangle must be right angled. Since all of the lengths given are integers, it follows that this triangle is a Pythagorean Triple. We know that 12 and either 9 , 8 must be the dimensions of the rectangle, since they are the largest lengths.

If we assign the shortest side, 5, to be the hypotenuse of the triangle, we see the 5-4-3 triple.

So the sides of complete rectangle are 12 and 9.

Area of pentagon = Area of Rectangle - Area of Triangle.

                               = 12 * 9 - 1/2*4*3

                                = 108 - 6

                                 = 102.

Ratio of Area of Pentagon to rectangle = 102 : 108

                                                                 =  17 : 18