act-dog

A. Incorrect. Use the Pythagorean theorem to calculate the missing side lengths in △ABE and △CDE. Start by using $7^2+{\left(DC\right)}^2={25}^2$ to calculate $DC=\sqrt{{25}^2-7^2}=24$ cm. Note that $DC=AB$ because opposite sides of a rectangle are equal. Then, use ${\left(AE\right)}^2+{24}^2={26}^2$ to calculate $AE=\sqrt{{26}^2-{24}^2}=10$ cm. You may have stopped here, but remember the problem asks you to solve for $BC$.

B. Incorrect. Use the Pythagorean theorem to calculate the missing side lengths in △ABE and △CDE. You may have used incorrect proportional reasoning and thought that since $BE=CE+1$, it had to be true that $AE=DE+1=8$. Then, you may have calculated $7+8=15$.

C. Correct. Use the Pythagorean theorem to calculate the missing side lengths in △ABE and △CDE. Start by using $7^2+{\left(DC\right)}^2={25}^2$ to calculate $DC=\sqrt{{25}^2-7^2}=24$ cm. Note that $DC=AB$ because opposite sides of a rectangle are equal. Then, use ${\left(AE\right)}^2+{24}^2={26}^2$ to calculate $AE=\sqrt{{26}^2-{24}^2}=10$ cm. Note that $AD=BC$ because opposite sides of a rectangle are equal. Since $AD=AE+DE$ and $AD=BC$, it is also true that $BC=AE+DE=10+7=17$ cm.

D. Incorrect. Use the Pythagorean theorem to calculate the missing side lengths in △ABE and △CDE. Start by using $7^2+{\left(DC\right)}^2={25}^2$ to calculate $DC=\sqrt{{25}^2-7^2}=24$ cm. Note that $DC=AB$ because opposite sides of a rectangle are equal. You may have stopped here, but remember the problem asks you to solve for $BC$.