Question

if △cdg ~ △edf, find the value of x. (the diagram shows triangle cdg and triangle edf with intersecting sides, labeled with lengths 48, 40, 2x + 7, and 5x - 2 at point d.)

Explanation:

Step1: Set up proportion of sides

$\frac{48}{2x+7} = \frac{40}{5x-2}$

Step2: Cross-multiply to eliminate fractions

$48(5x-2) = 40(2x+7)$

Step3: Expand both sides

$240x - 96 = 80x + 280$

Step4: Isolate x terms

$240x - 80x = 280 + 96$

Step5: Simplify and solve for x

$160x = 376$
$x = \frac{376}{160} = \frac{47}{20} = 2.35$

Answer:

$x = \frac{47}{20}$ or $x=2.35$