Question

The hypotenuse of a grassy land in the shape of a right triangle is 1 metre more than twice is the shortest side. if the third side is 7 metres more than the and shortest side, find the sides of the grassy land.

Answer 1

Answer:let the shortest side be x

Then hypotenuse=2x+1

Another side=7+x

By pythagoras theoram

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

Now solve its easy

Step-by-step explanation:

Answer 2

$\huge{\boxed{\mathbb{ANSWER}}}$

QUADRATIC EQUATION PROBLEM SOLVING!

TO FIND : The sides of the grassy land.

Let us assume that the shortest side = " x " metres

Hypotenuse = ( 2x + 1 ) metres

Third side = ( x + 7 ) metres

By using pythagoras theorem we have :-

( 2x + 1 )² = x² + ( x + 7 )²

4x² + 4x + 1 = 2x² + 14x + 49

2x² - 10x - 48 = 0

x² - 5x - 24 = 0

x² - 8x + 3x - 24 = 0

x ( x - 8 ) + 3 ( x - 8 ) = 0

( x - 8 ) ( x + 3 ) = 0

x = 8 or x = -3  

( negative one is not possible )

So, x = 8

ATLAST, I AM CONCLUDING MY WHOLE ANSWER :-

$\implies\boxed{\mathsf{The\:lengths\:of\:the\:sides\:of\:the\:grassy\:land\:are\:8metres,\:17metres\:and\:15metres.\:}}$