Question

A rectangular carpet has area 120 sq metre and perimeter 46 mtr. the length of its diagonal is ?

Answer 1

SoluTion :-

Let the length of carpet = a and breadth = b

 

Then,

$\sf {2(a + b) = 46 \Rightarrow a + b = 23}\\\\\\\sf {ab = 120}$

$\sf {\therefore Diagonal = \sqrt{a^{2}+b^{2}}}\\\\\\\\\sf {\rightarrowtail \sqrt{(a+b)^{a}-2ab} }\\\\\\\sf {\rightarrowtail \sqrt{23^{2}-240} }\\\\\\\sf {\rightarrowtail \sqrt{529-240} }\\\\\\\sf {\rightarrowtail \sqrt {289}}\\\\\\\sf {\rightsquigarrow 17\ metre}$

Answer 2

Answer:

17

Step-by-step explanation:

Given =》

Area= 120sq m

perimeter =46m

To Find =》

Length of diagonal =?

Solution =》

Let the length of carpet = X m

And, let the breadth = Y m

Area of rectangle =l×b

X×Y =120------------(1)

Perimeter of rectangle =2(l+b)

2(x+y)= 46

$x + y = \frac{46}{2} \\ = x + y = 23.........(2)$

From eq 1 and 2 by solving

x=15m or 8m

y= 8m or 15m

Length of diagonal =

$\sqrt{15 {}^{2} + 8 {}^{2} } \\ = \sqrt{225 + 64} \\ = \sqrt{289} \\ = 17m$

Hence, the length of diagonal is 17m