The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle. The two acute angles along the straight angle are congruent to each other. The overlapping part of the legs is labeled 20. The part of the overlapping side that extends above the smaller triangle is labeled 8. The leg of the smaller triangle that is a ray of the straight angle is labeled 3 x. The leg of the larger angle that is a ray of the straight angle is labeled 4 x plus 2.

Question

Mathematics

Tatiana

22 March, 16:08

The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle. The two acute angles along the straight angle are congruent to each other. The overlapping part of the legs is labeled 20. The part of the overlapping side that extends above the smaller triangle is labeled 8. The leg of the smaller triangle that is a ray of the straight angle is labeled 3 x. The leg of the larger angle that is a ray of the straight angle is labeled 4 x plus 2.

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Nicholas Mcmahon · Answer 1

x = 4

Given the description of the triangles, you have 2 similar right triangles. The smaller triangle has a height of 20 and a base of 3x, while the larger has a height of (20+8) = 28 and a base of 4x + 2. We wish to determine the value of x. Since the triangles are similar, the ratio of corresponding sides will be a constant. So:

20/28 = (3x) / (4x+2)

(4x+2) 20/28 = (3x)

(20/28) * 4x + (20/28) * 2 = (3x)

(80/28) * x + (40/28) = (3x)

(20/7) * x + 4/7 = 3x

4/7 = 3x - (20/7) * x

4/7 = (21/7) x - (20/7) * x

4/7 = x/7

4 = x

So the value of x is 4.