Question

A rope is fixed between two trees that are 8 m a part , when a child hangs on to the centre of the ripe it sags so that the centre is 3 m below the level of the ends. find the length of rope ​

Answer 1

$\huge{\underline{\underline{\mathbb\star\:Solution}}}</p><p>$

To find :

the length of rope

Step by step explanation

The length of rope = 2h

Here , h denotes to hypotenuse

ATQ

${(h})^{2} = {(b)}^{2} + {(p)}^{2} \\ h = \sqrt{ {(4)}^{2} + {(3)}^{2} } \\ h = \sqrt{16 + 9} \\ h = \sqrt{25} \\ h = 5$

${\large{\boxed{The \: length \: of \: rope = 2(5)m = 10m}}}$

Answer 2

Answer:

Distance between the two trees=8m

distance of child lagged(centre of the rope) =3m

Step-by-step explanation:

it forms one big triangle and if we divide the triangle equally it is divided into two right angles triangles

Base²+Height² = Hypotenuse²

for first triangle,

4²+3²=hypotenuse²

Hypotenuse =√25

hypotenuse =5m

as they are equilaterally divided they are congruent

length of the rope= 5x2=10m

Therefore, length of the rope =10m