Mathematics
helpplease151
19

"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"

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(2) Answers
rubydooby17

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

awintrev6117

Correct answer is D. [latex]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= \frac{8}{9} a_2 \\ \\b_1= \frac{8}{9} b_2 \\ \\c_1= \frac{8}{9} c_2 \\ \\ \frac{P_1}{P_2}= \frac{a_1+b_1+c_1}{a_2+b_2+c_2} = \frac{\frac{8}{9}a_2+\frac{8}{9}b_2+\frac{8}{9}c_2}{a_2+b_2+c_2} =\frac{\frac{8}{9}(a_2+b_2+c_2)}{a_2+b_2+c_2} =\frac{8}{9}[/latex] [latex]A_1= \frac{a_1b_1}{2} \\ \\A_2= \frac{a_2b_2}{2} \\ \\ \frac{A_1}{A_2} = \frac{\frac{a_1b_1}{2} }{\frac{a_2b_2}{2} } = \frac{a_1b_1} {a_2b_2 } =\frac{ \frac{8}{9} a_2\frac{8}{9} b_2} {a_2b_2 } =\frac{8}{9} \times \frac{8}{9} =\frac{64}{81} [/latex]

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