Question

Find the lengths of the diagonals of this trapezoid.

Answer 1

Answer: Length of diagonal from point (-b,c) to (a,0) is
`√((a+b)^2+c^2)`

Length of diagonal from point (b,c) to (-a,0) is
`√((a+b)^2+c^2)`

Step-by-step explanation:

The distance formula to find the distance between points (x,y) and (p,q) is given by :-

`d=√((x-p)^2+(y-q)^2)`

The length of diagonal from point (-b,c) to (a,0) is given by :-

`d=√((-b-a)^2+(c-0)^2)\\\\\Rightarrow\ d=√((-1)^2(a+b)^2+c^2)\\\\\Rightarrow\ d=√((a+b)^2+c^2)`

The length of diagonal from point (b,c) to (-a,0) is given by :-

`d=√((b-(-a))^2+(c-0)^2)\\\\\Rightarrow\ d=√((a+b)^2+c^2)`

Hence, the lengths of the diagonals of the given trapezoid is same as =
`√((a+b)^2+c^2)`