Two triangle are similar. The side of one are three times as long as the sides of the other. What is the ratio of the areas of the smaller to the larger?

Correct  A₁ : A = 1 : 9

Step-by-step explanation:

Given:  a = 3 a₁

Side of the first triangle let be a and of the second a₁

Area of the first triangle let be A and of the second A₁

If the two triangles are similar then it is:

A₁ : A = a₁² : a²  

A₁ : A = a₁² : (3 a₁)² = a₁² : 9 a₁² = 1 : 9

A₁ : A = 1 : 9

God is with you!!!

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

answer: 1, 3 and 5 are correct

step-by-step explanation: