Question

Manuel is planting a garden in the shape of a right triangle. The longer leg is 3 ft longer than the shorter leg. The hypotenuse is 3 for longer than the longer leg. Find the lengths of the three sides of the garden

Answer 1

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

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 from Right angled Triangle method

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