Question

The area of a rectangle with perimeter 40cm is 75cmsquare .find the length and breath of the rectangle​

Answer 1

Answer:

length is 15 cm and breadth is 5 cm.

Step-by-step explanation:

let length is X and breadth is y

then perimeter=40

2(x+y)=40

(x+y)=20

X=20-y

and area=75

x*y=75

(20-y)*y=75

y=5 or 15

and X= 15 or 5

but length is greater than breadth

therefore length is 15 cm and breadth is 5cm.

Answer 2

GivEn:

• Perimeter of Rectangle : 40 cm

• Area of Rectangle : 75 cm²

To find:

• Length and breadth of Rectangle.

SoluTion:

$\bf We\;have = \begin{cases} & \text{Perimeter of Rectangle = \bf{40 cm}} \\ & \text{Area of Rectangle = \bf{75cm^2} } \end{cases}$

As we know that,

$\maltese\;{\boxed{\sf{\pink{Perimeter\;of\; Rectangle\;:\;2(l + b)}}}}\\\\ \dashrightarrow\sf 2(l + b) = 40\;cm\\\\ \dashrightarrow\sf l + b = \cancel{ \dfrac{40}{2}}\\\\ \dashrightarrow\sf l + b = 20\\\\ \dashrightarrow\sf l = (20 - b)\;cm\qquad\bigg\lgroup\bf eq.\;1 \bigg\rgroup$

Now,

$\maltese\;{\boxed{\sf{\purple{Area\;of\; Rectangle\;:\;l \times b}}}}\\\\ \dashrightarrow\sf l \times b = 75\;cm^2\\\\ \;\;\dag\;\sf \underline{Put\;the\;value\;l\;from\;eq.\;1}\\\\ \dashrightarrow\sf (20 - b) \times b = 75\\\\ \dashrightarrow\sf 20b - b^2 = 75\\\\ \dashrightarrow\sf - b^2 + 20b - 75 = 0\\\\ \dashrightarrow\sf b^2 - 20b + 75 = 0\\\\ \dashrightarrow\sf b^2 - 5b - 15b + 75 = 0 \\\\ \dashrightarrow\sf b( b - 5) - 15(b - 5) = 0\\\\ \dashrightarrow\sf (b - 5)(b - 15) = 0\\\\ \sf \;\;\dag\;\sf \underline{Both\;(b - 5)\;and\;(b - 15)\;is\;equal\;to\;0.}\\\\ \sf Therefore,\\\\ \dashrightarrow\sf (b - 5) = 0\;;\;(b - 15) = 0\\\\ \dashrightarrow\sf b = 5\;;\;b = 15\\\\ \dashrightarrow\bf b = 5,15$

$\rule{150}2$

★ Now, Put the value of b in eq. (1) -

$\dashrightarrow\sf l = (20 - 15)\;,\; (20 - 5)\\\\ \dashrightarrow\bf l = 5\;;\;15$

As we know that,

★Length of Rectangle is always greater than its breadth.

$\therefore$ Breadth of Rectangle cannot be 15 cm if its length is 5 cm.

$\sf\dag\; {\underline{\sf{\red{Hence,\; Length\;of\; Rectangle\;is\;15\;cm\;and\;it's\;breadth\;is\;5\;cm}}}}.$