Question

solve for x. the triangles in each pair are similar. type your answer in the boxes hint: if you got 72, subtract 30

Explanation:

Step1: Set up similarity proportion

Since the triangles are similar, the ratios of corresponding sides are equal:
$\frac{12x - 5}{44} = \frac{90}{40}$

Step2: Simplify the right-hand ratio

Reduce the fraction $\frac{90}{40}$ to lowest terms:
$\frac{90}{40} = \frac{9}{4}$

Step3: Cross-multiply to solve for x

Cross-multiply to eliminate fractions:
$4(12x - 5) = 44 \times 9$
$48x - 20 = 396$

Step4: Isolate the variable term

Add 20 to both sides of the equation:
$48x = 396 + 20$
$48x = 416$

Step5: Solve for x

Divide both sides by 48:
$x = \frac{416}{48} = \frac{26}{3} \approx 8.67$

Answer:

$x = \frac{26}{3}$ or $x \approx 8.67$