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. the image shows right triangle abc with right angle at b, and a perpendicular segment bd from b to ac, with angle at c and a both 45 degrees. the length of ad is 7, and ac is 14. the tiles available are 14√3, 14√2, 7√2, 7√3, 14, 7. we need to match bc and bd to the correct tile lengths.

Explanation:

Step1: Find length of CD

Since $AC=14$ and $AD=7$, $CD = AC - AD = 14 - 7 = 7$

Step2: Analyze $\triangle BDA$

$\triangle BDA$ is a 45-45-90 triangle, so $BD=AD=7$

Step3: Calculate length of BC

In $\triangle BCD$, use Pythagoras: $BC=\sqrt{CD^2+BD^2}=\sqrt{7^2+7^2}=\sqrt{98}=7\sqrt{2}$

Answer:

$BC \longrightarrow 7\sqrt{2}$
$BD \longrightarrow 7$