Question

A tree is supported by a wire anchored in the ground 5 feet from its base.
The wire is 1 foot longer than the height that it reaches on the tree. Find
the length of the wire.​

Answer 1

Answer:

the length of the wire = 13 feet

Step-by-step explanation:

Let say Length of Wire = L ft

The wire is 1 foot longer than the height that it reaches on the tree

=> Height of tree it reaches = L - 1   ft

=> Perpendicular Height = L - 1 ft

wire anchored in the ground 5 feet from its base.

=> Base = 5 ft

Hypostenuse² = Base² + Length²

=> L² = 5² + (L - 1)²

=> L² = 25 + L² + 1 - 2L

=> 2L = 26

=> L = 13

the length of the wire = 13 feet

Answer 2

Answer :-

Length of the wire is 13 feet

Explanation :-

[Refer to the attachment for the figure]

Let the consider the figure line segments formed as a traingle i.e Δ ABC

Tree is supported by a wire anchored in ground 5 feet from its base

So Base of the Δ ABC (AB) = 5 feet

Let the height of the tree (AC) be 'x' feet

Length of the wire (BC) = 1 foot more than the height of the tree = (x + 1) feet

Figures with heights are considered as right angled triangles

So Δ ABC is a right angled triangle.

By Pythagoras theorem

AC² + AB² = BC²

⇒ x² + 5² = (x + 1)²

⇒ x² + 25 = (x)² + 2(x)(1) + (1)²

[ ∵ (a + b)² = a² + b² + 2ab]

⇒ x² + 25 = x² + 2x + 1

⇒ x² + 25 - x² = 2x + 1

⇒ 25 = 2x + 1

⇒ 25 - 1 = 2x

⇒ 24 = 2x

⇒ 24/2 = x

⇒ 12 = x

⇒ x = 12

Height of the tree = x = 12 feet

Length of the wire = (x + 1) = (12 + 1) = 13 feet

∴ the length of the wire is 13 feet.