Question

the area of a rectangular carpet is 120m² and the perimeter is 46m.what is the length of its daigonal​

Answer 1

Answer: 17m

Step-by-step explanation:

Given that perimeter of a rectangular carpet = 46m.

2(l + b) = 46

l + b = 23 ---------- (1)

Given that Area of a rectangular carpet = 120m^2.

l * b = 120 ------------ (2)

We know that length of the diagonal

root l^2 + b^2

= root (l + b)^2 - 2lb

= root(23)^2 - 2 * 120

= root 529 - 240

= root 289

= 17.

Therefore the length of the diagonal = 17m.

Hope this helps!

Answer 2

$\mathfrak{Question:}$

The area of a rectangular carpet is 120 m² and the perimeter is 46 m. What is the length of its diagonal?

$\mathfrak{Solution:}$

let the length and breadth of a rectangular carpet ​be l meter and b meter respectively.

So, Area = l×b m² = 120 m².......(i)

And perimeter = 2(l+b) m = 46 m .......(ii)

$\mathfrak{According\;to\;eq....(ii)}\\\\\implies\tt{2(l+b)=46}\\\\\implies\tt{l+b=\dfrac{46}{2}}\\\\\therefore\;\tt{l+b=23}$

a² + b² = (a+b)² - 2 ab

So, l² + b² = (l+b)² - 2 lb

After putting the value of eq(i) & eq(ii), we get

$\implies\tt{l^2+b^2=(23)^2-2.120}\\\\\implies\tt{l^2+b^2=529-240}\\\\\therefore\tt{l^2+b^2=289}$

$\bb{\tt{Diagonal=\sqrt{l^2+b^2}^ }}\\\\\tt{=\sqrt{289} =17 \;m.}$