Answer:

2(x+7)km

Step-by-step EXPLANATION:

Given information: AC⊥CB, AC = 2x km and CB = 2(x+7) km.

Pythagoras theorem: In a right angled triangle

hypotenuse^2=leg_1^2+leg_2^2hypotenuse

2

=leg

1

2

+leg

2

2

USING Pythagoras in triangle ABC,

(AB)^2=(AC)^2+(CB)^2(AB)

2

=(AC)

2

+(CB)

2

(26)^2=(2x)^2+(2(x+7))^2(26)

2

=(2x)

2

+(2(x+7))

2

676=4x^2+4x^2+56x+196676=4x

2

+4x

2

+56x+196

0=8x^2+56x-4800=8x

2

+56x−480

Taking out GCF.

0=8(x^2+7x-60)0=8(x

2

+7x−60)

Splitting the MIDDLE term we get

0=8(x^2+12x-5x-60)0=8(x

2

+12x−5x−60)

0=8(x(x+12)-5(x+12))0=8(x(x+12)−5(x+12))

0=8(x+12)(x-5)0=8(x+12)(x−5)

Using zero product property we get

x+12=0\Rightarrow x=-12x+12=0⇒x=−12

x-5=0\Rightarrow x=5x−5=0⇒x=5

The value of x is either -12 or 5.

If x=-12, then

AC=2x=2(-12)=-24AC=2x=2(−12)=−24

The distance can not be negative. So the only possible value of x is 5.

If x=5 then

AC=2x=2(5)=10AC=2x=2(5)=10

CB=2(x+7)=2(5+7)=2(12)=24CB=2(x+7)=2(5+7)=2(12)=24

The distance between A and B before the Constitution of highway.

AB=AC+CB=10+24=34AB=AC+CB=10+24=34

The distance between A and B after the Constitution of highway is 26 km. So, the distance saved after the Constitution of highway is

34-26=834−26=8

Therefore, the distance of 8 km will be saved.