Question

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? Check all that apply.
0.5(x)(x + 2) = 24

x(x + 2) = 24

x2 + 2x – 24 = 0

x2 + 2x – 48 = 0

x2 + (x + 2)2 = 24

x2 + (x + 2)2 = 100

Please help me quickly, I really need the help. I'll even mark brainiest if you do it correctly. I really need this and I need whoever does this to pay attention to the whole "Check all that apply". I'm adding the picture below.

Answer 1

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)

Answer 2

Area = 1/2 length times width
24 = 1/2 x(x + 2) = 0.5(x)(x + 2) 
24=x^2 +2x or x^2 + 2x - 24 = 0
answer

0.5(x)(x + 2) 
x^2 + 2x – 24 = 0 
x^2 + (x + 2)2 = 100