the diagonal of a rectangular field is 60m more than its
shortest side if its longest side is 30 metre more than the shorter side then find the area of the field ....answer plzz
Answers
Answer:
let say a rectangular field ABCD.
let the shortest side = AB
diagonal AC = 60m + AB
longest side = 30m
let the longest side be BC
Step-by-step explanation:
In a triangle ABC Right angled at B
by using pythogoras theorem :
AC^2 = AB^2 + BC^2
(60+AB)^2 = AB^2 + (30)^2
(60)^2 + (AB)^2 + 2(60)(AB) = AB^2 + 900
3600 + AB^2 + 120AB = AB^2 + 900
(HERE AB^2 WILL BE CANCELED BY AB^2)
3600 - 900 = 120AB
2700 = 120AB
2700 / 120 = AB
22.5m = AB
THEREFORE AC = AB + 60 = 22.5 + 60 = 82.5m
Thus area of the Field = L X B = 30 X 22.5 = 675m
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Answer:
Let the longer side be " l "
And the shorter side be " b"
A.t.q
Diagonal of rectangle = b+60 m
And the longer side = b + 30 m
Area of rectangle= lb
= (B+30)b
= B'2 + 30b .....
As the diagonal of rectangle divides it into two equal triangles
Therefore,
Area of rectangle= area of 2equal triangles
As angle of rectangle is 90°
=> Both the triangles are RT angled
Triangles
Height of each triangle 1/2 the diagonal
= b+60/2
Area of 1 triangle = 1/2 *b*h
= 1/2 * b+ 30 * b +60 /2
=(b +30 ) ( b+ 60 )/4