Question

a rectangular garden 50m long and 34m wide is surrounded by a uniform dirt road. find the width of the road if the total area is 540m²
​

Answer 1

Step-by-step explanation:

l = 50 m

b = 34 m

Perimeter = 2(l+b)

=2(50m+34m)

=2*84m

=168m

Area is 34m*50m

=1700m²

Hope it helps you

Answer 2

The width of the dirt road is 16 m.

Given:

A rectangular garden 50m long and 34m wide is surrounded by a uniform dirt road.

To Find:

The width of the road if the total area is 5400m².

Solution:

Let us consider the case of the garden alone.

The length of the garden = 50m

The width of the garden = 34m.

Hence, the area of the garden (which is in the shape of a rectangle)

= length x width = 50 x 34 = 1700m².

Now, a uniform dirt road surrounds the rectangular garden, such that the area of the garden along with the dirt road = 5400m².

Since the dirt road is uniform, let us assume that its width = y m.

The dirt road has extensions on two sides of the length as well as the width of the garden.

Hence, the new dimensions of the entire area (garden + road) then turn out to be:

The new length, l' = (50+2y).

The new length, w' = (34+2y).

⇒ The new area = l' x w' = (50+2y) x (34+2y).

⇒ 5400 = (50+2y) x (34+2y).

⇒ y² + 42y - 925 = 0

Let us use completing the square method to find out the required factors. The coefficient of y = 42.

Taking half of it becomes 42/2 = 21. Squaring 21 and adding it to both sides we get,

y² +42y + 441 = 925 + 441

⇒ (y+21)² = 1366

⇒ (y+21) = √1366 ≈ 37

⇒ y = 16

Hence the width of the dirt road is 16 m.

#SPJ2