Question

A rectangular carpet has an area of 120m square and it perimeter is 46m, the length of a diagonal is

Answer 1

Answer:

17

Step-by-step explanation:

Area of the rectangle = 120 m2

Perimeter = 46 m

Let the sides of the rectangle be l and b.

Therefore

Area = lb = 120 m2 …(1)

Perimeter = 2 (l + b) = 46

Or, (l + b) = 46 / 2 =23 m …(2)

Now, length of the diagonal of the rectangle = l^2 + b^2

So, we first find the value of (l^2 + b^2)

Using identity:

(l^2 + b^2) = (l + b)^2 – 2 (lb) [From (1) and (2)]

Therefore

(l^2 + b^2) = (23)^2 – 2 (120)

= 529 – 240 = 289

Thus, length of the diagonal of the rectangle = l^2 + b^2 = 289 = 17 m

Hope it helps u.

Answer 2

perimeter= 2(l+b) =46m
=>(l+b) =23

Area = lb =120m²

Now, (l+b)² = (l-b)² + 4lb
=> (l - b)² = (l+b)² - 4lb
=(23)² - 4× 120
=529 - 480=49
So, l-b = 49½ =7

l - b = 7
l + b= 23
-------------------
=> 2l = 30
=> l =15 & b =8

Diagonal = ( l²+b²) ½
= (15²+ 8²)½
=(289)½
=17 m