Question

the length of a rectangular field is greater than its width by 10 if the area of the field is 144 square metre find its dimensions solve the quadratic equation word problem​

Answer 1

Answer:

The length is 18 m

The width is 8 m

Step-by-step explanation:

Let,

The width of rectangular field (w) = y

The length of rectangular field (l) = y + 10

The area of the field is 144 square metre

So,

The area of rectangular field = length × width

⇒ y (y + 10) = 144

⇒ y² + 10y = 144

⇒ y² + 10y - 144 = 0

⇒ y² + 10y - 144 = 0

⇒ y² + 18y - 8y - 144 = 0

⇒ y (y + 18) - 8 (y + 18) = 0

⇒ (y + 18) (y - 8) = 0

⇒ y = - 18 Or y = 8

Hence,

⇒ y = 8

The width of rectangular field (w) = 8 m

__________________________

★ The length of rectangular field (l) = y + 10

⇒ 8 + 10

⇒ 18

The length of rectangular field (l) = 18 m

Therefore,

The length is 18 m

The width is 8 m

Answer 2

Given:-

• Length of rectangular field is greater than its width by 10

• Area of field = 144m²

To find:-

• Dimensions of field = ?

Solution:-

Let the width of field be (x)m

Then , the length of field will be (x + 10)m

As we know that,

Area of rectangle = length × width

144m² = x(x+10)

144 = x² + 10x

0 = x² + 10x - 144

0 = x² + 18x - 8x - 144

0 = x(x+18) - 8(x+18)

0 = (x+18)(x-8)

Now, either x = 8 or x = -18

Side can never be negative so x does not equal to -18

So , x = 8

Now the side will be

Width = 8cm

Length = (x+ 10) = (8+10)cm = 18cm

Hence , the side of rectangular field is 8cm, 18cm

Hope its help uh❤