a garden is 15 m × 10 m . It has a 2.6. m wide flower bed all around outside it. There is also a 2.5 m wide grassy path all around and outside the flower bed . Find the area of the flower bed and grassy path respectively​

flower bed = 157.04

grassy path = 202

Step-by-step explanation:

If you draw this out, it's basically a rectangle inside a rectangle inside a rectangle. I'm going to call those rectangles A, B, and C. with A being the smallest and C being the biggest.

first we need to find the area of A, B, and C.

A will be easy because we're already given that its 15x10

Area A = 150

To find area B, we need to add the 2.6 pathway to all the sides, so it'll be:

length: 15+2.6(2) = 20.2 m

width: 10+2.6(2) = 15.2 m

Area B = 307.04

Then we do the same for area C but with 2.5 m.

length: 20.2+2.5(2) = 25.2 m

width: 15.2+2.5(2) = 20.2 m

Area C = 509.04

To find the area of just the flower bed, we need to subtract area A from area B, then to find grassy path we need to subtract area B from area C.

flower bed: 307.04-150 = 157.04

grassy path: 509.04-307.04 = 202

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.