Question

the length of a rectangle is 5cm less than its length .if the length is increased by 4cm and the breadth is increased by 6cm,the area of a rectangle is found to increase by 140 sq .cm.find the length and breadth of the rectangle

Answer 1

Answer:

Assuming that breadth (and not length as in your question) of the rectangle is 5cm less than its length.

Let the length of the rectangle be x and breadth be y.

According to the question:-

y+5 = x     (The breadth of the rect. is 5cm less than its length so if we add 5 to the breadth then it will become equal to the length)   ..........(1)

And

(x+4)(y+6) = xy+140   ⇒  xy+6x+4y+24 = xy+140 ⇒ 6x+4y = 116 .........(2)  

eq(1) x 4 ⇒ 4y+20 = 4x ⇒ 4x-4y = 20 ...........(3)(eq 1 and 3 are same but for understanding I named them distinctly)

Adding (2) and (3):-

6x+4y = 116     ____(2)

4x-4y = 20     ____(3)

10x = 136 ⇒ x = 13.6

Keeping the value of x in eq 1:-

y+5 = 13.6 ⇒ y = 8.6

I hope this helps.

Answer 2

$\huge\sf\pink{Answer}$

☞ Length = 13.6 cm

☞ Breadth = 8.6 cm

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Length if a rectangle is 5 cm less than its breadth (mistake in Question)

✭ Length is increased by 4 cm

✭ Breadth is increased by 6 cm

✭ Area of the rectangle increases by 140 cm²

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

➢ Length and breadth of the triangle?

$\rule{110}1$

$\huge\sf\purple{Steps}$

❍ Let the length of the rectangle be x cm. Then, it's breadth = (x - 5) cm.

❍ Area of rectangle = x(x - 5) cm²

☆ If the length is increased by 4 cm and breadth is increased by 6 cm, area of rectangle is increased by 140 sq cm.

Increased length = (x + 4) cm

Increased breadth = (x - 5 + 6) cm = (x + 1) cm

Increased area = (x² - 5x + 140) cm²

$\sf\underline{\bullet{Area\: of \:rectangle = Length × Breadth}}$

➳ x² - 5x + 140 = (x + 4)(x + 1)

➳ x² - 5x + 140 = x² + 4x + x + 4

➳ x² - 5x + 140 = x² + 5x + 4

➳ x² - 5x + 140 - x² - 5x - 4 = 0

➳ -10x + 136 = 0

➳ -10x = - 136

➳ $\sf x = \dfrac{136}{10}$

➳ x = 13.6

Now,

$\circ\sf\orange{Length \:of \:rectangle\: = x = 13.6 \:cm}$

$\circ\sf\orange{Breadth \:of \:rectangle\: = x - 5 = 8.6 \:cm \:cm}$

$\rule{170}3$