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A wire is (7x - 3) metres long. A length of (3x - 4) metres is cut for use. If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed

Solution:

Given, a wire is (7x - 3) m long

A length of (3x - 4)m is cut for use

We have to find the length of wire left.

Length of wire left = total length of wire - length of wire cut for use

= (7x - 3) - (3x - 4)

= 7x - 3 - 3x + 4

By combining like terms,

= 7x - 3x - 3 + 4

By distributive property,

= (7 - 3)x + (-3 + 4)

= (4)x + (1)

= 4x + 1

Therefore, the length of wire left is 4x + 1 metres.

Given, the left out wire is used for making an equilateral triangle

We have to find the length of each side of the triangle so formed.

We know that an equilateral triangle has all sides of same length

Perimeter of wire = 4x + 1

Perimeter of triangle = sum of all sides

So, 3(side) = 4x + 1

Side = (4x + 1)/3

Therefore, the length of each side of the equilateral triangle is (4x + 1)/3 metres.

✦ Try This: The length of a rectangle plot is 6 m less than thrice its breadth. Find the dimensions of the plot if its perimeter is 148 m

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 12

NCERT Exemplar Class 7 Maths Chapter 10 Problem 83 (b)

A wire is (7x - 3) metres long. A length of (3x - 4) metres is cut for use. If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed

Summary:

A wire is (7x - 3) metres long. A length of (3x - 4) metres is cut for use. If this left out wire is used for making an equilateral triangle. The length of each side of the triangle formed is (4x + 1)/3 metres

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