Question

the area of a rectangle carpet is 120 m

and it's perimeter is 46m.the length of its diagonal is​

Answer 1

Answer:

5,520

Step-by-step explanation:

We have:

area of rectangle=120

perimeter=46

first we multiply them 120*46=5,520

Hence the length of it's diagonal is 5,520

Answer 2

Given,

The area of a rectangle carpet is $120m^{2}$ and its perimeter is $46m$

We have to find the length of its diagonal

Formula,

Area of rectangle $=lb$

Perimeter of rectangle $= 2(l+b)$

Now,

$2(l+b)=46$

$l+b=23$____(1)

And

$lb=120$

Now,

We know that

$(a-b)^{2} =(a+b)^{2} -4ab$

Here,

$a=l, b= b$

$(l-b)^{2} =(l+b)^{2} -4lb$

Now substitute the values in the above formula,

$(l-b)^{2} =(23)^{2}-4\times120$

$(l-b)^{2} =529-480$

$(l-b)^{2} =49$

$l-b=\sqrt{49}$

$l-b=7$____(2)

Now, subtract equation (2) from equation(1)

$l+b-l+b=23-7$

$2b=16$

$b=8$

Substitute $b=8$ in equation (2)

$l-b=7$

$l-8=7$

$l=7+8$

$l=15$

Here, we have to find the diagonals length

Formula for diagonals of rectangle

Diagonal $= \sqrt{l^{2}+b^{2} }$

$= \sqrt{15^{2}+8^{2} }$

$= \sqrt{225+64}$

$=\sqrt{289}$

$=17m$

Therefore, the length of its diagonal is $17m$.