Question

What are the values of a and b?

Answer 1

a = 400/21, b = 580/21

Explanation:

Small triangles are similar. Therefore, the sides are proportional

`(a)/(20)=(20)/(21)` cross multiply

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

`a=(400)/(21)`

For b, we can use the Pythagorean theorem:

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