Question

three triangles are used to compose a rectangle. what is the value of x? 21 square units, 9 square units, x square units. 16, 30, 32, 60

Explanation:

Step1: Recall rectangle - triangle area relationship

The area of a rectangle is divided into three non - overlapping triangles. The sum of the areas of these three triangles is equal to the area of the rectangle. Also, the area of a rectangle is given by the product of its length and width. In a rectangle, if we consider two non - overlapping right - angled triangles formed by a diagonal, the sum of the areas of any two non - overlapping triangles that make up the rectangle has a certain relationship. In this case, the two given triangles and the unknown triangle make up the rectangle. The area of a rectangle is split among the three triangles. We know that the sum of the areas of the three triangles is the area of the rectangle. And for a rectangle, the sum of the areas of two non - overlapping triangles that cover the whole rectangle is equal to the area of the rectangle. Here, the sum of the areas of the three triangles is the area of the rectangle. So, \(x+9 + 21\) is the area of the rectangle. Also, we know that in a rectangle, the sum of the areas of two non - overlapping triangles that cover the whole rectangle is equal to the area of the rectangle. So \(x=21 + 9\).

Step2: Calculate the value of \(x\)

\(x=21+9\)
\(x = 30\)

Answer:

30