The Lengths of the Sides of δ Abc Are Consecutive Integers. It δ Abc Has the Same Perimeter as an Equilateral Triangle with a Side of Length 9 Cm, What is the Length of the Shortest Side of δAbc? - Mathematics

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The lengths of the sides of Δ ABC are consecutive integers. It Δ ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?


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We are given that triangle ABC has equal perimeter as to the perimeter of an equilateral triangle having side 9 cm. The sides of triangle ABC are consecutive integers. We are asked to find the smallest side of the triangle ABC 

Perimeter of an equilateral triangle, say having side 9 cm is given by

p = 3a 

a = 9 cm 

p = 3 × 9 

p = 27 cm 

Let us assume the three sides of triangle ABC be x, x+1, x−1

Perimeter of triangle ABC, say Pis given by

P1 = AB + BC + AC

AB = x; BC = x +1; AC = x−1. Since P1 P. So

`p_1 = p`

`27 = x + ( x+1) + (x-1) `

`27 = 3x`

`x = 27/3 `

x  =  9 cm 

By using the value of x, we get the sides of triangle as 8 cm, 9 cm and 10 cm

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals
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RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.4 | Q 11 | Page 25

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