Question

What is the value of x? Enter your answer in the box. x = cm A bow tie shape polygon made of two bow ties that share a vertex. The shape is created by two segments intersecting forming two triangles with vertical angles. An alternate interior angle of the triangles are marked congruent to each other. The larger triangle is on the left and the smaller triangle is on the right. In the larger triangle, the left side of the triangle is 32 centimeters. The south side of the triangle is 40 centimeters. On the smaller triangle, the right side of the triangle is 4 centimeters. The north side of the triangle is labeled x.

Answer 1

side x is 5 cm long

Explanation:

Use proportions, given that the two triangles are similar because they contain three equal angles:

One angle due to connected by the vertex (oppose by the vertex), another angle as marked with the tick, and the third one has to be the same due to the fact that the addition of the three internal angles of a triangle must equal 180 degrees.

Then our proportion becomes:

`(4)/(32) =(x)/(40)`

And then we solve for x by multiplying both sides by 40 (to eliminate the denominator on the right):

`(4)/(32) =(x)/(40) \\(4*40)/(32) =x\\ x=5\,\,cm`