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.
However, if the length of this rectangle
increases by 3 units and the breadth by
2 units, the area increases by 67 square units.
Find the dimensions of the rectangle.​

Answer 1

HEY MATE YOUR ANSWER IS HERE.....

LET THE LENGTH BE = X

AND BREATH BE = Y

THEN AREA = XY

NOW ACCORDING TO THE QUESTION.....

CASE 1

BREATH INCREASED BY 3 UNITS

LENGTH REDUCES BY 5 UNITS

AND THUS AREA GET REDUCED BY 9 sq UNITS

SO

( X - 5 ) ( Y + 3 ) = XY - 9

XY + 3X - 5Y - 15 = XY - 9

HENCE

3X - 5Y = 6 -------- Eq 1

NOW IN CASE 2

LENGTH INCREASED BY 3 UNITS

AND BREATH INCREASED BY 2 UNITS

AREA WILL INCREASED BY 67 sq UNITS

SO

( X + 3 ) ( Y + 2 ) = XY + 67

XY + 2X + 3Y + 6 = XY + 67

2X + 3Y = 61 -------- Eq 2

NOW FROM EQUATION 1 AND 2

SUBSTITUTION METHOD

FROM EQUATION 1 VALUE OF X

$x = \frac{5y + 6}{3} \: \: \: \: \: \: be \: eq \: 3$

now put the value of X in eq 2

$2( \frac{5y + 6}{3} ) + 3y = 61 \\ \\ \frac{10y + 12}{3} + 3y = 61 \\ \\ \\ \frac{10y + 12 + 9y}{3} = 61 \\ \\ 19y + 12 = 183 \\ \\ 19y = 171 \\ \\ \\ y = 9$

★ HENCE VALUE OF Y = 9 ★

NOW PUT THE VALUE OF Y IN EQUATION 3

$x = \frac{5(9) + 6}{3} \\ \\ x = \frac{45 + 6}{3} \\ \\ x = \frac{51}{3} \\ \\ x = 17$

★ HENCE THE VALUE OF X = 17 ★

SO

LENGTH (X) = 17 UNITS

BREATH (Y) = 9 UNITS

THANKS FOR UR QUESTION HOPE IT HELPS

★ KEEP SMILING ☺️✌️ ★