Question

the perimeter of a rectangle is 104 m and its
area is 640 m². Find its length and breadth..​

Answer 1

Answer:

l=20

b=32

Step-by-step explanation:

2(l+b)=104

now, transfer 2 from LHS to RHS

l+b= 104/2= 52

now we can conclude l+b=52

l×b=640 (this is area)

l+b=52

l×b=640

20+32=52

20×32=640

therefore l=20 ,b=32

Answer 2

${ \red{ \huge{ \boxed{ \bold{ \underline{ \: solution}}}}}}$

Given :-

▪ the perimeter of a rectangle is 104 m and its area is 640 square m.

To Find :-

▪ length and breadth of the rectangle??

■》let the length ( l ) of the rectangle be x m.

for a rectangle,

${ \boxed{ \bold{ \: area \: = \: length \times breadth}}}$

${ \bold{ \implies{ \: 640 \: {m}^{2} = x \: \times \: breadth}}}$

${ \bold{ \implies{ \: breadth(b) \: = \: \frac{640}{x} m}}}$

${ \boxed{ \bold{ \: perimeter \: = 2( \: l \: + \: b \: )}}}$

${ \bold{ \implies{104 \: m \: = 2(x \: + \frac{640}{x} )}}}$

${ \bold{ \implies{(x + \frac{640}{x} ) = 52}}}$

${ \bold{ \implies{ \frac{( {x}^{2} + 640)}{x} = 52}}}$

${ \bold{ \implies{ {x}^{2} + \: 640 = \: 52x}}}$

${ \bold{ \implies{ {x}^{2} \: - \: 52x \: + \: 640 \: = \: 0}}}$

${ \bold{ \implies{ {x}^{2} - (32x + 20x) + 640 = 0}}}$

${ \bold{ \implies{ {x}^{2} - 32x - 20x + 640 = 0}}}$

${ \bold{ \implies{ x(x - 32) - 20(x - 32) = 0}}}$

${ \bold{ \implies{ (x - 20)(x - 32) = 0}}}$

=》 x = 20 m , 32m

• If we take x = 20 m = length

then, breadth = 640/x = 640/ 20 = 32m

while , when x = 32m = length

breadth = 640/ 32 = 20m

☆HoPE iT hELpS you