Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.
determine each segment length in right triangle abc
triangle abc with right angle at b, bd perpendicular to ac, angle at c and a is 45 degrees, ad = 7, ac = 14, tiles: 7√3, 7√2, 14√2, 14√3, 7, 14; need to pair bc and bd with correct tile

Explanation:

Step1: Find CD length

$CD = AC - AD = 14 - 7 = 7$

Step2: Analyze △BDC

△BDC is 45-45-90 right triangle, so $BD = CD = 7$

Step3: Calculate BC

$BC = BD\sqrt{2} = 7\sqrt{2}$ (45-45-90 triangle hypotenuse rule)

Answer:

BC: $7\sqrt{2}$, BD: 7