Question

What are the values of a and b?

Answer 1

Answer:

a = 400/21, b = 580/21

Step-by-step explanation:

Small triangles are similar. Therefore, the sides are proportional

$\dfrac{a}{20}=\dfrac{20}{21}$               cross multiply

$21a=(20)(20)$       divide both sides by 21

$a=\dfrac{400}{21}$

For b, we can use the Pythagorean theorem:

$b^2=\left(\dfrac{400}{21}\right)^2+20^2\\\\b^2=\dfrac{160000}{441}+400\\\\b^2=\dfrac{160000}{441}+\dfrac{176400}{441}\\\\b^2=\dfrac{336400}{441}\to b=\sqrt{\dfrac{336400}{441}}\\\\b=\dfrac{\sqrt{336400}}{\sqrt{441}}\\\\b=\dfrac{580}{21}$