Can someone help me find the ratio for the sides of this triangle?

Question

Ella Armstrong · Accepted Answer

As detailed below.

Given #DE# parallel #AB# Consider triangles CDE & CAB. #hat(CDE) = hat(CAB)# ( corresponding angles. #hat(CED) = hat(CBA)# ( corresponding angles. #hat C# common. Hence, two triangles are similar. #:. (AC) / (DC) = (BC) / (EC) = (AB) / (DE)# Eqn (1) (6.) but #AC = AD + DC# and #BC = (BE + EC)# #:. (AD+ DC) / ((DC) = (BE + EC) / (EC)# #(AD) / (DC) + cancel1 = (BE) / (EC) + cancel1# #(AD) / (DC) = (BE) / (EC)# But given #(AD) / (DC) = 1/3# #:. (EB) / (EC) = 1/3# or #(EC) / (EB) = 3 / 1 = 3# (7.) Measurements are known for #AB, AD, BC# Substituting in (1), #(color(purple )(AD) + DC) / (DC) = color(purple)(BC) / (EC) = color(purple)(AB) / (DE)# Hence, at least one more side measurement is needed to find the lengths of other sides.

Sadie Allen · Answer

undefined To find the ratio for the sides of a triangle, you typically look at the lengths of the sides in relation to each other. Without specific measurements provided, it's difficult to determine the ratio. If you provide the lengths of the sides of the triangle, I can help you find the ratio.