Please help!! I don't understand how to do this

The distance of the support post from the front of the house is 8 feet

Step-by-step explanation:

Let us revise some important rules in the right triangle

If EDF is a right triangle where D is the right angle and DG ⊥ EF where G lies on EF, then

Look to the attached figure for more understanding

Let us use the first rule to solve the problem

Assume that the distance from the front of the house to the post is x feet

∵ The distance from the front to the back of the house is 26 feet

∵ The distance from the front of the house to the post is x feet

∴ The distance from the post to the back of the house = 26 - x feet

In the figure we have right triangle and the post is perpendicular from the right angle to the floor which is opposite to the right angle, so we can use the first rule above

∵ The post is 12 feet tall

∴ (12)² = x × (26 - x)

- Simplify the two sides

∴ 144 = x(26) - x(x)

∴ 144 = 26x - x²

- Add x² to both sides

∴ x² + 144 = 26x

- Subtract 26x from both sides

∴ x² - 26x + 144 = 0

Now let us factorize the left hand side into two factors

∵ x² = (x)(x)

∵ 144 = (-8)(-18)

∵ -8x + -18x = -26x

- That means the factors are (x - 8) and (x - 18)

∴ The factors of x² - 26x + 144 are (x - 8) and (x - 18)

∴ (x - 8)(x - 18) = 0

Equate each factor by 0 to find x

∵ x - 8 = 0

- Add 8 to both sides

∴ x = 8

OR

∵ x - 18 = 0

- Add 18 to both sides

∴ x = 18

∴ The values of x are 8 and 18

The distance from the front of the house to the post is less than the distance from the post to the back of the house

That means the distance from the front of the house to the post is 8 feet and the distance from the post to the back of the house = 26 - 8 = 18 feet

The distance of the support post from the front of the house is 8 feet

true !

step-by-step explanation:

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