∆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 units. The ratio of the area of ∆ABC to the area of ∆DEF is .

1/100

Step-by-step explanation:

the problem description is not copied fully.

but I think I understand it.

since the ratio of the perimeter is 1/10, so is then also the ratio for each side.

that means the longest side of ABC is 4 units (40/10), right ?

anyway, when the ratio of lengths and distance is 1/10, then the ratio for the area is 1/10×1/10 = 1/100.

because for the area (baseline × height / 2) two lengths have to be multiplied. and that multiplies the scaling factor twice into the calculation effectively squaring it as the area scaling factor.

and 1/10×1/10 = (1/10)² = 1/100