Question

The area of a rectangle gets reduced by 9 square units, if its length is reduced by
5 units and breadth is increased by 3 units. If we increase the length by 3 units and
the breadth by 2 units, the area increases by 67 square units. Find the dimensions
of the rectangle.​

Answer 1

$\huge\sf\red{Solution}$

☯ Let's consider length and breadth of a rectangle be x and y units respectively.

Then,

Area of Rectangle = xy sq. units

━━━━━━━━━━━━━━━━⠀

Now,

★ According to the Question:

Thee area of rectangle gets reduced by 9 square units If its length is reduced by 5 units and breadth by is increased by 3 units.

${\bold{\sf\green{➯ xy - 9 = (x - 5)(y + 3)}}}$

${\bold{\sf\green{➯ xy - 9 = xy + 3x - 5y - 15}}}$

${\bold{\sf\green{➯ - 9 = 3x - 5y - 15}}}$

${\bold{\sf\green{➯ 3x - 5y = - 9 + 15}}}$

${\bold{\sf\green{➯ 3x - 5y = 6}}}$

${\bold{\sf\green{➯ - 5y = 6 - 3x}}}$

${\bold{\sf\green{➯ y = - (6 - 3x)/5}}}$

${\bold{\sf\green{➯ y = (3x - 6)/5}}}$ ⠀⠀⠀⠀⠀⠀⠀⠀❬ eq(1) ❭

And,

If we increase the length by 3 units and breadth by 2 units, the area increases by 67 square units.

${\bold{\sf\blue{➯ (x + 3)(y + 2)=xy + 67}}}$

${\bold{\sf\blue{➯ xy + 2x + 3y + 6 = xy + 67}}}$

${\bold{\sf\blue{➯ 2x + 3y + 6 = 67}}}$

${\bold{\sf\blue{➯ 2x + 3y = 67 - 6}}}$

${\bold{\sf\blue{➯ 2x + 3y = 61}}}$ ⠀⠀⠀⠀⠀⠀⠀⠀❬ eq(2) ❭

━━━━━━━━━━━━━━━━⠀

✇ Now, Putting eq (1) in eq (2),

${\bold{\sf\pink{➯ 2x + 3{(3x - 6)/5} = 61}}}$

${\bold{\sf\pink{➯ 2x + (9x - 18)/5 = 61}}}$

${\bold{\sf\pink{➯ (10x + 9x - 18)/5 = 61}}}$

${\bold{\sf\pink{➯ 10x + 9x - 18 = 61 × 5}}}$

${\bold{\sf\pink{➯ 19x - 18 = 305}}}$

${\bold{\sf\pink{➯ 19x = 305 + 18}}}$

${\bold{\sf\pink{➯ 19x = 323}}}$

${\bold{\sf\pink{➯ x = 323/19}}}$

${\bold{\sf\pink{➯ x = 17}}}$

━━━━━━━━━━━━━━━━

✇ Now, Putting value of x in eq (1),

${\bold{\sf\purple{➯ y = (3 × 17 - 6)/5}}}$

${\bold{\sf\purple{➯ y = (51 - 6)/5}}}$

${\bold{\sf\purple{➯ y = 45/5}}}$

${\bold{\sf\orange{➯ y = 9}}}$

∴ Hence, The length and breadth of rectangle is 17 units and 9 units respectively.

Answer 2

Answer:

happy chocolate day abhinav whats_app par baat kar fir

deti hu par direct answer ko report karo