Question

Find the area of the triangle

Answer 1

Answer: 20x+3

Explanation:
We find the area of a triangle by multiplying and then dividing by 2. In this problem, I decided to split the triangle in half. So now. We have two equations to find area.
3x(2x)(5)
2x(x+6)(5)
Multiplying the first problem, we get 30x. With the second problem, we get 10x+6. Adding these areas, we get 40x+6. Though, we have to divide by two because it is a triangle. That is how I got my answer of 20x+3

Answer 2

Answer:

A ≈ 14.079 square units

Step-by-step explanation:

Area of a triangle is one half the base times the height.

A = ½ bh

A = ½ (10) (2x)

A = 10x

We need to find the value of x.

Starting with the triangle on the left, use Pythagorean theorem to find the length of the base.

(3x)² = (2x)² + a²

9x² = 4x² + a²

a² = 5x²

a = x√5

Repeat for the triangle on the right:

(x + 6)² = (2x)² + b²

x² + 12x + 36 = 4x² + b²

b² = -3x² + 12x + 36

The two bases add up to 10:

a + b = 10

Subtract a from both sides, then square both sides:

b = 10 − a

b² = 100 − 20a + a²

Substitute and simplify:

-3x² + 12x + 36 = 100 − 20(x√5) + 5x²

0 = 64 − (12 + 20√5) x + 8x²

0 = 2x² − (3 + 5√5) x + 16

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ (3 + 5√5) ± √((-(3 + 5√5))² − 4(2)(16)) ] / 2(2)

x = [ (3 + 5√5) ± √(9 + 30√5 + 125 − 128) ] / 4

x = [ (3 + 5√5) ± √(6 + 30√5) ] / 4

x ≈ 1.4079, 5.6823

If we substitute 5.6823 into our a and b equations, we find that a = 12.706 and b = 7.322, which add up to 20.028, not 10.

So x ≈ 1.4079.

Therefore the area is:

A ≈ 14.079