Question

The hypotenuse of a right-angled triangle is 17 cm and the difference

between other two sides is 7 cm. Find the other two unknown sides.​

Answer 1

Let the other two sides be x and x-7

H²=P²+B²

17²=x²+(x-7)²

[USING (a-b)²=a²+b²-2ab]

289=x²+x²+49-14x

289-49=2x²-14x

240=2x²-14x

2x²-14x-240=0

2(x²-7x-120)=0

x²-7x-120=0

x²-15x+8x-120=0

x(x-15)+8(x-15)=0

(x+8)(x-15)=0

x+8=0

x= -8(rejected)

x-15=0

x=15

Length of other two sides.

x = 15cm

x - 7 = 15 - 7 = 8cm

Answer 2

Answer:

BC= 8 cm

AB = 15 cm

Step-by-step explanation:

AB - BC = 7

AB = 7 + BC

By pythagoras theorem

AC^2= AB^2+BC^2

17^2=(7+BC)^2+BC^2

289=49+BC^2+14BC + BC^2

2BC^2+ 14 BC -240=0

2 BC^2 +30 BC - 16 BC -240=0

(2 BC - 16) (BC+ 15)

BC= 8 cm

AB = 15 cm