Question

solve for x given the following similar triangles.
image of two similar triangles, first triangle has sides 11x - 4 (with one tick mark), 70 (with two tick marks); second triangle has sides 60 (with one tick mark), 50 (with two tick marks)
options:

• x = 16
• x = 84
• x = -5
• x = 8

Explanation:

Step1: Set up proportion of sides

$\frac{11x-4}{60} = \frac{70}{50}$

Step2: Simplify the right-hand side

$\frac{11x-4}{60} = \frac{7}{5}$

Step3: Cross-multiply to eliminate fractions

$5(11x-4) = 7 \times 60$

Step4: Expand and simplify both sides

$55x - 20 = 420$

Step5: Isolate the variable term

$55x = 420 + 20$
$55x = 440$

Step6: Solve for x

$x = \frac{440}{55}$

Answer:

x = 8