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. a x2 + 2x – 24 = 0 b x(x + 2) = 24 c x2 + (x + 2)2 = 100 d 0.5(x)(x + 2) = 24 e x2 + 2x – 48 = 0 f x2 + (x + 2)2 = 24

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)