Question

"The figures are similar. The ratio of the lengths of their corresponding sides is 40:45, or 8:9. Find the ratio of their perimeters and the ratio of their areas. The figures are not drawn to scale.

A) 9:10 and 81:100 .. B) 8.9 and 81:100 .. C) 9:10 and 64:81 .. D) 8.9 and 64:81"

Answer 1

write a story ending in with the statement we apologized to each other and reconciled

Answer 2

Correct answer is D.


`P_1=a_1+b_1+c_1 \\ \\ P_2=a_2+b_2+c_2 \\ \\a_1:a_2=b_1:b_2=c_1:c_2=8:9 \\ \\a_1= (8)/(9) a_2 \\ \\b_1= (8)/(9) b_2 \\ \\c_1= (8)/(9) c_2 \\ \\ (P_1)/(P_2)= (a_1+b_1+c_1)/(a_2+b_2+c_2) = ((8)/(9)a_2+(8)/(9)b_2+(8)/(9)c_2)/(a_2+b_2+c_2) =((8)/(9)(a_2+b_2+c_2))/(a_2+b_2+c_2) =(8)/(9)`


`A_1= (a_1b_1)/(2) \\ \\A_2= (a_2b_2)/(2) \\ \\ (A_1)/(A_2) = ((a_1b_1)/(2) )/((a_2b_2)/(2) ) = \frac{a_1b_1} {a_2b_2 } =\frac{ (8)/(9) a_2(8)/(9) b_2} {a_2b_2 } =(8)/(9) * (8)/(9) =(64)/(81)`