Question

1. Is it possible to draw a triangle, the lengths of whose sides are given below?
(i)lcm, lcm, lcm (ii) 2cm, 3cm, 4cm (iii) 7cm, 8cm, 15cm (iv) 3.4cm, 2.1cm, 5.3cm (v) 6cm. 7cm, 14cm​

Answer 1

To find :

• Whether a triangle can be formed with given set of length of sides

Method used :

• Sum of any two side of triangle should be greater than 3rd side
• Generally we take it as , sum of two smaller side should be more than the largest side

If above mentioned condition is fulfilled than the triangle can be formed with given set of sides

Solution :

(i) 1cm , 1cm , 1cm

• as all side are equal we can take sum of any two side
• (1+1) = 2 > 1 { third side }

Hence, a triangle can be formed with these side

(ii) 2cm, 3cm, 4cm

• here all side are unequal so we will take sum of two smaller sides
• (2+3) = 5 > 4 { third side }

Hence, a triangle can be formed with these side

(iii) 7cm, 8cm, 15cm

• here all side are unequal so we will take sum of two smaller sides
• (7+8) = 15 = 15 { third side }

Hence, a triangle cannot be formed with these side

(iv) 3.4cm, 2.1cm, 5.3cm

• here all side are unequal so we will take sum of two smaller sides
• (2.1 + 3.4) = 5.5 > 5.3 { third side }

Hence, a triangle can be formed with these side

(v) 6cm. 7cm, 14cm

• here all side are unequal so we will take sum of two smaller sides
• (6+7) = 13 < 14 { third side }

Hence, a triangle cannot be formed with these side

ANSWER :

Triangle can be formed by using (i) (ii) & (iv)

Traingle cannot be formed by using (iii) & (v)