Question

What is the length of RP?

Answer 1

Answer:

RP = 8 units

Step-by-step explanation:

(x + x + 2) * (x + 2) = (4 + 6) *4

(2x + 2) * (x + 2) =10 * 4

2(x + 1)(x + 2) = 40

(x + 1)(x + 2) = 40/2

= x^2 + 2x + x + 2 = 20

= x^2 + 3x + 2 = 20

= x^2 + 3x - 18 = 0

= x^2 + 6x - 3x - 18 = 0

= x(x + 6) - 3(x + 6) = 0

= (x - 3)(x + 6) = 0

So x = 3, - 6

We know that the length can't be -ve because it's a dimension  

So, x = 3

We know that RP = x + 2 + x

So RP = 3 + 2 + 3

= 8

Hope this helps, and please mark me brainliest if it does!

Answer 2

Answer:

RP = 14

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

(x+x+2) * (x+2) = (4+6)*4

Combine like terms

(2x+2)(x+2)=10*4

2(x+1)(x+2) = 40

Divide by 2

(x+1)(x+2) = 20

FOIL

x^2+2x+x+2 = 20

x^2 +3x+2 =20

Subtract 20

x^2 +3x-18 = 0

Factor

(x +9) (x-6) = 0

Using  the zero product property

x+9=0   x-6 =0

x= -9    x=6

Since the length cannot be negative

x=6

RP = x+2+x = 6+2+6 = 14