Question

diagonal of a rectangular field is 17 metre and perimeter is 46 metre then area of the field will be​

Answer 1

Step-by-step explanation:

length of field = a

breadth of field =b

since perimeter of field is 46 we can say 2(a+b)=46

and a + b = 23

and a = 23 - b ##(i)

as the field is rectangular and diagonal is given we can consider a right angled triangle with height = a

base = b

and hypotenuse = diagonal =17

applying pythagoras theorem we get

(a*a) + (b*b) = (17*17)

using value of a from ##(i)

we get

(23-b)(23-b) +(b*b) = (17*17)

[529+(b*b) -2*23*b] +(b*b) = 289

529 + (b*b) - 46b +(b*b) = 289

529-289 - 46b + 2(b*b) = 0

240 - 46b + 2(b*b) = 0

240/2 -(46b/2) +2(b*b)/2 = 0/2

120 - 23b + (b*b) = 0

now arrange them

(b*b) -23b + 120 = 0

(b*b) -15b - 8b + 120 = 0

b( b- 15) -8(b - 15) = 0

(b - 8) (b - 15) = 0

now (b-8 )= 0 OR( b-15) = 0

b = 8 , 15

now we got two values of b

try to find the perimeter you will get

2( a + b ) = 46

2 ( 15 + 8) = 46. [a,b = 15 , 8 ;not respective]

2 (23) = 46

46 = 46

means you git the sides and area is the product of the sides

area = 15 * 8

area = 120 meter square