What is the length of the third side of the window frame below? (figure is not drawn to scale.) a picture of a right triangular window frame is shown. the longest side has length labeled as 87 inches. the height of the frame is labeled as 63 inches.

60 inches

Step-by-step explanation:

Given: A frame in the shape of right triangle with the longest side = 87 inches

The height of the frame is labeled as 63 inches.

Let 'x' be the third side of the frame then by Pythagoras theorem of right triangle , we have

Hence, the length of the third side of the window frame = 60 inches.

3 is greater then both of those numbers

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)