Question

The hypotenuse of a right angled triangle is 6m more than twice of the shortest side if the third is 2m less than than hypotenuse find the sides of the trianhle

Answer 1

Let hypotenuse is H...smallest side is x and the other side is y
Now
H= 6 + 2x
y =H - 2
And H^2 = x^2 + y^2
Solving these 3 equations we get x=10...y=24 and H=24

Answer 2

Answer:

10cm (short side)

hypotenuse:  26cm

long side:  24cm

Step-by-step explanation:

Let x = shortest side

then

2x+6 = hypotenuse

2x+6-2 = 2x+4 = long side

.

x^2 + (2x+4)^2 = (2x+6)^2

x^2 + (2x+4)(2x+4) = (2x+6)(2x+6)

x^2 + 4x^2+16x+16 = 4x^2+24x+36

5x^2+16x+16 = 4x^2+24x+36

x^2+16x+16 = 24x+36

x^2-8x+16 = 36

x^2-8x-20 = 0

(x-10)(x+2) = 0

x {-2, 10}

throw out the negative solution leaving:

x = 10m (short side)

.

hypotenuse:

2x+6 = 2(10)+6 = 20+6 = 26m

.

long side:

2x+4 = 2(10)+4 = 20+4 = 24m