Question

If ΔABc ω ΔDEF where perimeter of Δ DEF is 30cm and its area is 45cm²

A.What is the constant of proportionality?
B.What is the ratio of their perimeter?
C.If BC =5cm ,thenhow long is EF?
D.What is the perimeter of Δ ABC?
E.What is the ratio of their area?
F.What is the area of Δ ABC?

PLEASE HELPPPPPPPPPPPPP

Answer 1

1. The perimeter of ΔABC is 30cm and the ratio of its perimeter to that of another triangle is 2:3. Therefore, the perimeter of the other triangle is (30*3)/2 = 45cm.

2. The constant of proportionality between the two triangles' areas is sqrt(25/9) = 5/3 because their perimeters are in a ratio of 2:3. Therefore, if the area of ΔABC is 45cm², then the area of the other triangle is (45*(5/3)^2) = 125cm².

3. The constant of proportionality between two sides in similar triangles is equal to their ratio. Since EF corresponds to PR in both triangles, we know that EF/PR = 10/x where x is the length of AC. Solving for x gives us x=15.

Therefore, AC has a length of 15cm.