1.5m tall boy stands at a distance of 3m from a lump post and cast a shadow of 4.5m on the ground.Find the height of lump post
did you make a sketch?
If so, you should see the ratio ...
h/7.5 = 1.5/4.5
h = 7.5(1.5)/4.5
= ...
2.5
To find the height of the lump post, we can use similar triangles and the concept of proportions.
Let's consider the triangle formed by the boy, the lamp post, and their respective shadows.
In this triangle, we have the following information:
- The height of the boy (h1) = 1.5m
- The length of the boy's shadow (s1) = 4.5m
- The distance from the boy to the lamp post (d) = 3m
Now, let's label the height of the lamp post as h2.
Using the concept of similar triangles, we can set up a proportion between the corresponding sides of the triangles:
h1 / s1 = h2 / s2
where s2 is the length of the lamp post's shadow. We know that s2 is equal to the distance from the lamp post to the boy plus the length of the boy's shadow. So, s2 = d + s1.
Now, substituting the given values into the equation, we have:
1.5 / 4.5 = h2 / (3 + 4.5)
1.5 / 4.5 = h2 / 7.5
To solve for h2, we can cross multiply:
1.5 * 7.5 = 4.5 * h2
11.25 = 4.5 * h2
Divide both sides by 4.5:
11.25 / 4.5 = h2
h2 = 2.5
Therefore, the height of the lamp post is 2.5 meters.