9. The hypotenuse of a 45°-45°-90° triangle is 5 sqrt 6. Find the length of one leg of the right triangle.

5 ✓ 3

Step-by-step explanation:

using Pythagoras Theory

(5 ✓ 6 )2 =, 2 x square side

square leg length= 150/ 2=, 75

length =5 ✓ 3

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)