Question

Find the length and breadth of a rectangle whose perimeter is 26m and area is 30m^2​

Answer 1

Answer:

perimeter=26m

2(l+b)=26m

l+b=13m

l=13-b   (1)

area=30m²

l*b=30

(13-b)b=30

13b-b²=30

b²-13b+30=0

b²-3b-10b+30=0

b(b-3)-10(b-3)=0

b-10)(b-3)=0

b-10=0   and b-3=0

b=10m or b=3m

if b=10m, l=13-10= 3m

if b=3m, l=13-3= 10m

Step-by-step explanation:

Answer 2

$\bf{\huge{\underline{\boxed{\rm{\green{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\red{Given:}}}}}$

• Perimeter of rectangle = 26 m
• Area of rectangle = 30 m²

$\bf{\underline{\underline{\sf{\red{To\:find:}}}}}$

• Length of the rectangle
• Breadth of the rectangle

$\bf{\underline{\underline{\sf{\red{Solution:}}}}}$

Let the length of the rectangle be x m.

Let the breadth of the rectangle be y m.

We know that perimeter of a rectangle is calculated using the formula,

$\bf{\large{\underline{\boxed{\rm{\green{Perimeter\:of\:rectangle\:=\:2(\:length\:+\:breadth)}}}}}}$

Substitute the given values,

=> 26 = 2 ( x + y)

=> 26 = 2x + 2y

Dividing throughout by 2,

=> 13 = x + y

=> x + y = 13

=> y = - x + 13 ----> 1

Now, we have the area of the rectangle. So by using the formula for area of a rectangle we will obtain our second equation.

We know that the area of the rectangle is calculated using the formula,

$\bf{\large{\underline{\boxed{\rm{\green{Area\:of\:rectangle\:=\:\:length\:\times\:breadth}}}}}}$

Plug in the values,

=> 30 = (x) (y)

Substitute value of y from equation 1,

=> (x) ( - x + 13) = 30

=> - x² + 13x - 30 = 0

Dividing throughout by -1,

=> x² - 13x + 30 = 0

=> x² - 10x - 3x + 30 = 0

=> x ( x - 10) - 3 ( x - 10) = 0

=> (x - 10) = 0 OR (x - 3) = 0

=> x - 10 = 0 OR x - 3 = 0

=> x = 10 OR x = 3

Length = x = 10 m OR 3 m

When x = 10,

Breadth = y = - x + 13

Breadth = y = - 10 + 13 = 3 m

When x = 3,

Breadth = y = - x + 13

Breadth = y = - 3 + 13 = 10 m

$\bf{\large{\underline{\boxed{\rm{\pink{Length\:of\:the\:rectangle\:=\:x\:=\:10m\:\:\:\:OR\:\:\:x\:=\:3m}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\pink{Breadth\:of\:the\:rectangle\:=\:y\:=\:3m\:\:\:\:OR\:\:\:x\:=\:10m}}}}}}$