a tree casts a 26-ft shadow.A boy standing nearby casts a 12-ft shadow, forming similar triangles. His height is 4.5 ft. How tall is the tree

Question

This question is a question I don't Know the answer to please help me.

Answer 1

in similar triangles, the corresponding or related angles in one triangle are congruent (equal) to the angles in the second triangle. However the corresponding sides are not equal. If they were, the triangles would be congruent rather than similar. However for similar triangles, the ratio of the corresponding or related sides is the same for all three pairs of sides. A ratio is a fraction. To solve this kind of problem we form two ratios and set them equal to each other. This is called a proportion.

 

For example   a/b = c/d    this can be read a is to b as c is to d

 

In this question, you set up a ratio between the shadow lengths and another ratio for the heights and set them equal. The one quantity we don't know and which we are asked to find is the height of the tree.

Let T = the height of the tree

 

Then     T/4.5 = 26/12         multiply both sides by 4.5 to isolate the variable T

 

T = (4.5)(26) / 12 = 9.75 feet

 

Answer 2

let x=height of the tree

x/4.5=26/12

12x=4.5*26

12x=117

x=117/12

x=9.75 feet is the height of the tree