Question

3) There is a square shaped land and a road with 6m width is situated along the 2 adjacent sides of the land.

I) If the length of a side a square land is X meters. Draw a sketch diagram to show above information.

II)Show that the area of the land with road is X2 + 12X +36

IV)Simplify the following expressions

i) X² +2X+4X+8 ii) (3+X) (6-X)​

Answer 1

i) Diagram is attached in the given image.

II) (x+6)² = x² + 12x + 36

IV)

i)   (x+4)(x+2)

ii) - x² + 3x + 18

What is a quadratic equation ?

A quadratic equation has a highest degree of 2 and have two values which satisfies ax² + bx +c = 0 also called the roots of the given equation.

According to the given question

Each side of the square is x meter is length and a road of 6 meter wide is situated along the two adjacent side of the square.

I) The square land with 6m wide road along the two adjacent side is drawn in the image attached.

ii) We know that the area of a square is product of it's two adjacent side.

∴The length of the two adjacent side with 6 meter wide road  is (x+6) meters each.

So, Area of the square land with 6 meter road on it's two adjacent side is

(x+6)²

= x² + 12x +36.

So it is same as given therefore satisfied.

IV)

i) x² + 2x + 4x + 8

 x(x+2)+4(x+2)

 (x+4)(x+2)

ii) (3+x)(6-x)

  18 -3x +6x - x²

 - x² + 3x + 18

Learn more about quadratic equations here :

https://brainly.com/question/17177510

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