Question

area of rectangle is 200 CM square and diagonal is 10√5 then find the dimension of the rectangle. ​

Answer 1

Answer:l = 20 and b=10

Step-by-step explanation:

Area of rectangle = lb = 200cm square

lb = 200........eqn. 1

Diagonal, d =10 sq. root 5

Using Pythagoras theorem

l^2 + b^2 = d^2

l^2 + b^2 = (10 sq. root 5)sq. = 500

l^2 + b^2 = (l + b)sq. - 2lb = 500

(l +b)sq. - 2(200) = 500

(l + b)sq. = 500 - 400

(l + b)sq. =100

(l + b) = sq. root (100)

= 10

l + b = 10

l = 10 - l........eqn.2

Substitute eqn. 2 in 1

(10 - l)l= 200

10b - l^2 = 200

l^2 - 10l - 200

l^2 + 10l - 20l - 200

l(l+ 10) - 20(l + 10)

(l + 10)=0. and (l - 20)=0

l= -10 and 20

Length can’t be negative

Therefore l =20

b = 20 - 10

b =10