Question

A RECTANGLE HAS DIMENSIONS 9 1/4 IN. Y 15 IN. a DIAGONAL OF THE RECTANGLE FORMS TWO MATCHING RIGHT TRIANGLES. WHAT IS THE AREA OF ONE OF THE TRIANGLES?

Answer 1

Let's call the length of the rectangle a, the width b, and the diagonal c. We know that a = 9.25 inches and b = 15 inches, and we can use the Pythagorean theorem to solve for c:

a^2 + b^2 = c^2
(9.25)^2 + (15)^2 = c^2
85.5625 + 225 = c^2
310.5625 = c^2
c = sqrt(310.5625)
c = 17.619 inches (approximately)

Now that we have the diagonal, we can find the area of one of the right triangles using the formula for the area of a triangle:

Area = (base * height) / 2

The base of the triangle is the width of the rectangle (15 inches), and the height is the length of the rectangle (9.25 inches):

Area = (15 * 9.25) / 2 = 138.75 / 2 = 69.375 square inches.

So the area of one of the right triangles is approximately 69.375 square inches.