△MNO ~△DEF. Identify the perimeter and area of △MNO to the nearest tenth. PLEASE HELP!!!

Option A: P ≈ 38.7 in, A ≈ 63.7 in²

Step-by-step explanation:

We are told that △MNO ~△DEF. This means that they are similar triangles.

We can solve for this using scale factor.

a) Perimeter of △MNO

The scale factor of two similar triangles is equal to the ratio of the perimeter of the triangles

Scale factor(k) = ratio of the sides of the triangles

In the diagram we are given

Side of △MNO = 6.7in

Side of △DEF = 9in

Perimeter of △MNO = X

Perimeter of △DEF = 52in

Scale factor (k) = 6.7/9

Hence,

6.7/ 9 = X/52

Cross Multiply

9X = 6.7 × 52

X = 6.7 × 52/9

X = 38.711111111 inches

To the nearest tenth, Perimeter of △MNO = 38.7 inches

b) Area of △MNO

The square of the scale factor of two similar triangles is equal to the ratio of area of the triangles

Scale factor(k) = ratio of the sides of the triangles

In the diagram we are given

Side of △MNO = 6.7in

Side of △DEF = 9in

Area of △MNO = Y

Area of △DEF = 115in²

Scale factor (k) = 6.7/9

Hence,

(6.7/ 9)² = Y/115

6.7²/9² = Y / 115

Cross Multiply

9² × Y = 6.7² × 115

Y = 6.7²× 115 /9²

Y = 63.732716049 square inches

To the nearest tenth, Area of △MNO = 63.7 in²

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total