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

The equation that can be used to find the lengths of the legs of the triangle is $\rm 0.5(x)(x + 2) = 24$

Given that

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

We have to determine

Which equations can be used to find the lengths of the legs of the triangle?

According to the question

From the given figure the base of the triangle is x.

And the height of the triangle is (x+2).

What is the area of a triangle?

The area of the triangle is given by half the product of the height and base.

$\rm Area = \dfrac{1}{2} \times base \times height$

Substitute all the values in the formula;

$\rm Area \ of \ right \ triangle= \dfrac{1}{2} \times base \times height\\ \\ \rm 24= \dfrac{1}{2} \times x \times (x+2)\\\\ \rm 0.5(x)(x + 2) = 24$

The equation can be used to find the lengths of the legs of the triangle is $\rm 0.5(x)(x + 2) = 24$.

Hence, the equation can be used to find the lengths of the legs of the triangle is $\rm 0.5(x)(x + 2) = 24$.

To know more about the Area of the Triangle click the link given below.

https://brainly.com/question/15442893