The area of the right triangle shown is 24 square feet.

Which equations can be used to find the lengths of the legs of the triangle? Select three options.

0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100

Given : A  = 24 sq feet

A = 0.5 base x height

base = x , height = x+2

A = 0.5 x(x+2)  = 24 sq feet

1) 0.5 x(x+2) = 24 (A)

2) x^2 + 2x - 48 = 0 (D)

To check the rest un-wrap the bracket:

x^2 + (x+2)^2 = 24

x^2 + x^2 + 4 + 4x = 24

2x^2 + 4x - 20 = 0

x^2 + 2x - 10= 0 (NO)

Likewise:

x^2 + (x+2)^2 = 100

x^2 + x^2  +4 + 4x = 100

2x^2 + 4x + 4 = 100

2x^2 + 4x - 96 = 0

3) x^2 + 2x - 48 = 0 (F)

To sum up: that's what apply:

1) 0.5 x(x+2) = 24 (A)

2) x^2 + 2x - 48 = 0 (D)

3) x^2 + 2x - 48 = 0 (F)