Question

a piece of land is in shape of right triangle the hypotenuse is 3m more than twice the shortest side if the perimeter of the piece of land is 6 times the shortest side find the dimensions of the piece of land​

Answer 1

Answer:

Let the length of the shortest side be x metres.

Then,

Hypotenuse = (2x+1) metres

Third side = (x+7) metres

By pythagoras theorem,

(2x+1)

2

=x

2

+(x+7)

2

4x

2

+4x+1=2x

2

+14x+49

2x

2

−10x−48=0

x

2

−5x−24=0

(x−8)(x+3)=0

x=8,−3

x=8 [x



=−3]

Hence, the lengths of the sides of the grassy land are 8 metres, 17 metres and 15 metres.

Answer 2

Answer:

Let the length of the shortest side be x metres.

Then,

Hypotenuse = (2x+1) metres

Third side = (x+7) metres

By pythagoras theorem,

(2x+1)2=x2+(x+7)2

4x2+4x+1=2x2+14x+49

2x2−10x−48=0

x2−5x−24=0

(x−8)(x+3)=0

x=8,−3

x=8        [x=−3]

Hence, the lengths of the sides of



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