15 A corner is cut off of a 9 by 9inch square piece ot paper

15. A corner is cut off of a 9- by 9-inch square piece ot paper. The cut is x inches trom a vertex as shown below. 9 in. a. Write an equation, in terms of x, that represents the area, A, of the paper after the corner is removed. 73 b. What value of x will result in an area that is of the area of the original square piece of 81 paper? Show how you arrived at your answer.

Solution

Actual area of the square without cut = 9*9 = 81

Area of the cut (triangle) = 1/2*(x*x) = (1/2)* x²

a).

AreaA, of the paper after the corner is removed = 81-(1/2)*x²

A = 81 - (1/2)*x²

b). According to the given information

81-(1/2)*x² = (73/81)*81

81 - (1/2)*x² = 73

(1/2)*x² = 8

x² = 16

x = 4