Paul walks 25 feet away from his house and places a mirror on the ground. he backs 5 feet away from the mirror so that he can see the tip of the roof. paul's eyes are 6 feet above the ground. paul and the house are both perpendicular to the ground. the angles between the top of the house, the mirror, and the ground and between paul's eyes, the mirror, and the ground are congruent as shown in the image below:
image depicts a mirror on the ground between a person and a house. the mirror is 5 feet away from the person and 25 feet away from the house.
what is the height of the house? show your work and explain your reasoning in complete sentences.

you have 2 similar triangles., the triangle formed from the mirror and paul and the triangle formed by the mirror and the house.

all the angles from one triangle are congruent to all the angles from the other triangle, which make the sides proportional.

the ratio of the sides for paul is 6/5

the ratio of the sides for the house is   x/25, where x is the height of the house.

now set the equations to equal each other and solve for x:

6/5 = x/25

cross multiply : (6*25) = (5*x)

simplify:

150 = 5x

divide both sides   by 5 to solve for x:

x = 150 / 5

x = 30 feet.

the house is 30 feet high.

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