Question

Given congruent triangles △RST ≅ △LMN where MN = 33, LN = 54, and RT = 4x + 6. Find the value of x.

A) x = 6
B) x = 8
C) x = 9
D) x = 10

Answer 1

To find the value of x in the given congruent triangles, we can set up a proportion using the corresponding sides. Solving the proportion equation will give us the value of x. In this case, x is equal to -3/2 or -1.5.

Step-by-step explanation:

Given congruent triangles △RST ≅ △LMN where MN = 33, LN = 54, and RT = 4x + 6. To find the value of x, we can set up the proportion:

33/54 = (4x + 6)/RT

Cross-multiplying, we get:

33(RT) = 54(4x + 6)

Simplifying further, we get:

33RT = 216x + 324

Combining like terms and rearranging the equation:

216x = 33RT - 324

Now, we can solve for x by dividing both sides by 216:

x = (33RT - 324)/216

We are given that RT = 4x + 6, so we substitute the value of RT in terms of x:

x = (33(4x + 6) - 324)/216

Simplifying the equation:

x = (132x + 198 - 324)/216

Combining like terms:

x = (132x - 126)/216

Multiplying both sides by 216 to eliminate the fraction:

216x = 132x - 126

Subtracting 132x from both sides:

84x = -126

Dividing both sides by 84:

x = -126/84

Simplifying the fraction:

x = -3/2

Therefore, the value of x is -3/2 or -1.5.