Question

The length of a rectangle exceeds the breadth by 5cm. If the length is decreased by 1 cm and the breadth is increased by 3 cm, then the area of the new rectangle increases by 32 cm². Find the dimensions of the original rectangle.​

Answer 1

Answer:

10 * 15 cm

Step-by-step explanation:

Suppose breadth of rectangle is X, than length would be X + 5

Values for new rectangle are X + 3 and X + 4 respectively

Area of first and second rectangle are A1 and A2 respectively

According to question

A1 + 32 = A2

X(X + 5) + 32 = (X + 3) (X + 4)

X² + 5X + 32 = X² + 7X + 12

2X = 20

X = 10

Put the value of X in both

Answer 2

$\huge\sf\red{\underbrace {\overbrace {\pink{answer}}}}$

Step-by-step explanation:

let the original length and breadth be l and b .

$\boxed {l\;=\;x}$

$\boxed {b\;=\;x\;+\;5}$

Now,

$\underline {new \;length \;=\;x\;-\;1}$

$\underline {new \;breadth \;=\;x\;+\;8}$

Area of new triangle exceeds the area of original triangle.

= (x-1) (x+8) = x(x+5) + 32

= x² + 8x - x - 8 = x² + 5x + 32

= 8x - x - 5x = 32 + 8

= 2x = 40

= x = 20 .

so,

$\huge\sf{Length \;=\;20}$

$\huge\sf{breadth \;=\;25}$

hope it helps you out.