Question

use the image to answer the question. if rectangle adcb has db = 26 and ab = 10, how long is $overline{cb}$? option #1: 16 option #2: 24 option #3: 28 option #4: 32

Explanation:

Step1: Apply Pythagorean theorem

In right - triangle $ABD$, if $DB$ is the hypotenuse and $AB$ and $AD$ are the legs. According to the Pythagorean theorem $DB^{2}=AB^{2}+AD^{2}$. In rectangle $ADCB$, $CB = AD$.

Step2: Solve for $AD$ (or $CB$)

We know that $DB = 26$ and $AB = 10$. Substitute these values into the Pythagorean formula: $AD=\sqrt{DB^{2}-AB^{2}}=\sqrt{26^{2}-10^{2}}=\sqrt{(26 + 10)(26 - 10)}=\sqrt{36\times16}=\sqrt{576}=24$. Since $CB = AD$ in rectangle $ADCB$, $CB = 24$.

Answer:

Option #2: 24