Bryan purchased two triangular wall shelves. the sides of each shelf are 8 inches, 10 inches, and 12 inches. he's trying to build a similar, larger triangular shelf to hang between the smaller ones. which of the dimensions can bryan use for the larger shelf so that it is similar to the ones he purchased? justify why the three triangles are similar.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .