Question

A triangle is drawn. three different squares are then drawn using the sides of the triangle as one side of each square. if the combined area of the squares on the two shorter sides is greater than the area of the square on the longest side, then the triangle is acute. 3 boxes outline a triangle. one box has an area of 100 inches squared and another box has an area of 36 inches squared. the third box has an area of question mark. the area of the square on the shortest side is 36 square inches. the area of the square on the longest side is 100 square inches. which is a possible value for the area of the square on the remaining side if the triangle is acute?

Answer 1

To determine a possible value for the area of the square on the remaining side of the triangle, we need to compare the areas of the two shorter squares to the area of the longest square.

Step-by-step explanation:

To determine a possible value for the area of the square on the remaining side of the triangle, we need to compare the areas of the two shorter squares to the area of the longest square. We know that the area of the square on the shortest side is 36 square inches, and the area of the square on the longest side is 100 square inches. Let's assume the area of the square on the remaining side is represented by x.

1. Area of the square on the shortest side = 36 square inches
2. Area of the square on the longest side = 100 square inches
3. Combined area of the squares on the two shorter sides > Area of the square on the longest side
4. 36 + 36 > 100
5. 72 > 100

Since the combined area of the squares on the two shorter sides is not greater than the area of the square on the longest side, the triangle is not acute.