Answer:
The length of shorter side of triangle is 9 cm
The length of longer side of triangle is 12 cm
The length of hypotenuse is 15 cm
Step-by-step explanation:
Given as , for the garden in the shape of right triangle :
Let The length of shorter side = B = x ft
So , the length of longer side = P = ( x + 3 ) ft
And The hypotenuse length = H = ( 3 + P ) ft
I.e H = ( 3 + x + 3 ) ft = ( x + 6 ) ft
Now<u> from Right angled Triangle method </u>
Hypotenuse² = Perpendicular² + Base²
Or, ( x + 6 )² = ( x + 3 )² + x²
Or, x² + 12 x + 36 = x² + 6 x + 9 + x²
Or, - x² + 6 x + 27 = 0
Or, - x² + 9 x - 3 x + 27 = 0
Or, - x ( x - 9 ) - 3 ( x - 9 ) = 0
So, ( x - 9 ) ( - x - 3 ) = 0
∴ x = 9 , - 3
So, shorter length = x = 9 cm
The longer length = x + 3 = 9 + 3 = 12 cm
The hypotenuse length = x + 6 = 9 + 6 = 15 cm
Hence The length of shorter side of triangle is 9 cm
The length of longer side of triangle is 12 cm
And The length of hypotenuse is 15 cm . Answer
