The triangles are similar. what is the value of x?

x = 13

Step-by-step explanation:

There are two ways to do this. You could use the Pythagorean Theorem because you are given that the triangles are right angled triangles.

Method One

a^2 + b^2 = c^2

a = 5

b = 12

c = ?

c^2 = 5^2 + 12^2

c^2 = 25 + 144

c^2 = 169

sqrt(c^2) = sqrt(169)

c = 13

x = 13

Method Two

You can do this problem with similar triangles.

48/12 = 52/x                    Cross multiply

48x = 12 * 52                   Combine the right  

48x = 624                        Divide by 48

48x/48 = 624/48              Do the division

x = 13  

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)