Question

these triangles are similar. solve for x. 84° 8 61° 14 x = ? x 61° 84° 7

Explanation:

Step1: Match corresponding sides

Identify matching sides: the side of length 8 in the large triangle corresponds to the side of length 7 in the small triangle; the side of length 14 in the large triangle corresponds to side $x$ in the small triangle. Set up a proportion for similar triangles:
$\frac{8}{7} = \frac{14}{x}$

Step2: Cross-multiply to solve for x

Cross-multiply to isolate $x$:
$8x = 14 \times 7$

Step3: Calculate and simplify

Compute the product, then solve for $x$:
$8x = 98$
$x = \frac{98}{8} = \frac{49}{4} = 12.25$

Answer:

$x = 12.25$ or $x = \frac{49}{4}$