Question

A fox and an eagle lived at the top of cliff of height 6m ,whose base was at a distance of 10m from a point a on ground . The fox descend the cliff and went straight to a point



a. The eagle flew vertically up to a height x metres and then flew straight line to a point a , the distance traveled by each being the same. Find the value of x.

Answer 1

Distance traveled by the fox = distance traveled by the eagle
(6+x) 2 + (10)2 = (16 – x)2
on solving we get
x = 2.72m.

Answer 2

Answer:

Value of x is 2.72

Step-by-step explanation:

Given: Height of the cliff = 6 m

          Distance between point a and Foot of Cliff = 10 m

          Fox descends direct to point a and Eagle first go straight up then then to point a.

         Fox and Eagle covered same distance.

To find: Distance that Eagle flew straight up.

Given distance eagle straight up is x

Figure is attached.

Distance that fox covered = 6 + 10 = 16 m

Distance that Eagle covered = $x+\sqrt{(6+x)^2+10^2}=x+\sqrt{36+100+12x+x^2}=x+\sqrt{x^2+12x+136}$

According to the question,

$x+\sqrt{x^2+12x+136}=16$

$\sqrt{x^2+12x+136}=16-x$

Squaring both sides,

$x^2+12x+136=16^2+x^2-32x$

12x + 136 = 256 - 32x

44x = 120

x = 2.72

Therefore, Value of x is 2.72