Two cross roads, each of width 8m, cut at right angles through the centre of a rectangular park of length 600m and breadth 340m and parallel to its sides. Find the area of the
roads. Also find the area of the park excluding cross roads.

Area(path)=7456sqm

Area(green)=196,544 sqmeters

Step-by-step explanation:

See image. The long path is

8×600=4800sqm

The short path is

8×340=2720sqm

But we've included the center square twice. So we should remove the redundancy by subtracting 64.see image

Area(paths)

=4800+2720-64

= 7456 sq meters

Area of the entire park= 600×340

=204,000 sq meters

Area(park not incl roads)=

204000 - 7456

=196,544 sq meters

it’s supposed to be -4+45=41

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240