∆ABC is similar to ∆DEF. The ratio of the perimeter of ∆ABC to the perimeter of ∆DEF is 1 : 10. The longest side of ∆DEF measures 40 units. The length of the longest side of ∆ABC is 241630 units. The ratio of the area of ∆ABC to the area of ∆DEF is 1 : 11 : 21 : 101 : 100.
Accepted Solution
A:
Answer:Part 1) The length of the longest side of ∆ABC is 4 unitsPart 2) The ratio of the area of ∆ABC to the area of ∆DEF is [tex]\frac{1}{100}[/tex]Step-by-step explanation:Part 1) Find the length of the longest side of ∆ABC we know thatIf two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factorThe ratio of its perimeters is equal to the scale factorLetz ----> the scale factorx ----> the length of the longest side of ∆ABC y ----> the length of the longest side of ∆DEFso[tex]z=\frac{x}{y}[/tex]we have[tex]z=\frac{1}{10}[/tex][tex]y=40\ units[/tex]substitute[tex]\frac{1}{10}=\frac{x}{40}[/tex]solve for x[tex]x=(40)\frac{1}{10}[/tex][tex]x=4\ units[/tex]thereforeThe length of the longest side of ∆ABC is 4 unitsPart 2) Find the ratio of the area of ∆ABC to the area of ∆DEFwe know thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredLetz ----> the scale factorx ----> the area of ∆ABC y ----> the area of ∆DEF[tex]z^{2}=\frac{x}{y}[/tex]we have[tex]z=\frac{1}{10}[/tex]so[tex]z^2=(\frac{1}{10})^2[/tex][tex]z^2=\frac{1}{100}[/tex]thereforeThe ratio of the area of ∆ABC to the area of ∆DEF is [tex]\frac{1}{100}[/tex]