Paragraph: Read the following information and answer: A B C D is a trapezium such that A B and C D are parallel and B C is perpendicular to them. Let A D B= , A B D= , B C=p and C D=q and C D=q . Question: What is A B equal to?

Step-by-step solution

From A B D , aligned & A B = B D (180^ -( + ) ) & A B= B D ( + ) = B D + aligned Again from B C D , aligned & B D= (B C)^2+(C D)^2 = p^2+q^2 & = B C B D = p p^2+q^2 & = C D B D = q p^2+q^2 aligned aligned A B & = p^2+q^2 p p^2+q^2 + q p^2+q^2 & = (p^2+q^2 ) p +q aligned