Question

The hypotenuse of a right triangle is 10cm long. If one leg is 2 units longer than the other leg, then how long is the longer leg?​

Answer 1

Answer:

in right angled triangle there is one property ,

square of hypotenuse = sum of squares of other two side

so ,

• here let one side length = l
• so another side is 2 units longer than first one .so length of another side= l+2
• so now, l^2 + (l+2)^2 = 10^2
• so , 2(l^2 )+ 4l + 4 = 100
• so, l^2 +2l - 48 =0
• so, l^2 +8l-6l -48=0
• so, we get l= -8 and l = 6, but negetive value of l is not possible because it is length of leg of triangle.
• so l=6 is one leg length and another leg length is 6+2=8.
• so l=6 is one leg length and another leg length is 6+2=8. so loner leg length is 8 units

Answer 2

Answer:

sides of triangle = 10 , x , x + 2

by pythagorous theoram ;

${10}^{2} = ({2x})^{2} + ({x})^{2} \\ 100 = 4 {x}^{2} + {x}^{2} \\ 100 = 5 {x}^{2} \\ {x}^{2} = \frac{100}{5} \\ x {}^{2} = 20 \\ x = \sqrt{20}$

hope it helps