Question

A farmer had some land of area 9x3y2z sq. m.
He divided it into equal parts of 3xy2z sq. m.
How many parts was the land divided into?

Answer 1

$\huge\bold{\mathtt{Question⇒}}$

A farmer had some land of area 9x³y²z sq. m. He divided it into equal parts of 3xy²z sq. m. How many parts was the land divided into?

$\huge\bold{\mathtt{Given⇒}}$

• Area of whole field = 9x³y²z m²

• Area of each part = 3xy²z m²

$\huge\bold{\mathtt{To\:find⇒}}$

The no. of parts.

$\huge\bold{\mathtt{Solution⇒}}$

Let the no. of parts be a.

We know that:

$\boxed{\tiny\mathtt{No.\:of\:parts×Area\:of\:each\:part=Area\:of\:whole\:field.}}$

According to condition,

$a × 3xy²z = 9x³y²z$

$⇒\:a = {\frac{9x³y²z}{3xy²z}}$

$⇒\:a = {\frac{9x³\cancel{y²z}}{3x\cancel{y²z}}}$

$⇒\:a = {\frac{9x³}{3x}}$

$⇒\:a = 3x²$

$\huge\bold{\mathtt{Hence⇒}}$

a = 3x²

No. of parts = a = 3x²

$\huge\bold{\mathtt{Therefore⇒}}$

The land was divided into 3x² parts.

$\huge\bold{\mathtt{Done}}$

$\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

$\large\bold{\mathtt{Have\:a\:nice\:day.}}$