Case study :
A teacher asked to Rohan to draw a triangle with following condition: The longest side of the triangle is 7 cm less than twice the shortest side and third side is 7 cm shorter than longest side. The perimeter of the triangle is atleast 84 cm.
Based on the above information, form a linear inequation and answer the following questions :
(i) What is the minimum length of the shortest side ?
(ii) What is the minimum length of the longest side ?
(iii) Identify the type of triangle that Rohan has drawn along with the length possible sides he got.
(iv) What is the least area of the triangle drawn ?

Question

Case study :
A teacher asked to Rohan to draw a triangle with following condition: The longest side of the triangle is 7 cm less than twice the shortest side and third side is 7 cm shorter than longest side. The perimeter of the triangle is atleast 84 cm.

A teacher asked to Rohan to draw a triangle with following condition: The longest side of the triangle is 7 cm less than twice the shortest side and third side is 7 cm shorter than longest side. The perimeter of the triangle is atleast 84 cm. Linear Inequations, Concise Mathematics Solutions ICSE Class 10.

Based on the above information, form a linear inequation and answer the following questions :

(i) What is the minimum length of the shortest side ?

(ii) What is the minimum length of the longest side ?

(iii) Identify the type of triangle that Rohan has drawn along with the length possible sides he got.

(iv) What is the least area of the triangle drawn ?

KnowledgeBoat · Accepted Answer

Let the shortest side of triangle be x cm. Given, Longest side of triangle = 2x - 7 Third side of triangle = (2x - 7) - 7 = 2x - 14 (i) Given, Perimeter of triangle is atleast 84 cm. ⇒ x + (2x - 7) + (2x - 14) 84 ⇒ 5x - 21 84 ⇒ 5x 84 + 21 ⇒ 5x 105 ⇒ x ⇒ x 21. Hence, minimum length of the shortest side of triangle = 21 cm. (ii) Length of the longest side of triangle = 2x - 7 Minimum length of longest side will be when x = 21, substituting value we get : ⇒ 2(21) - 7 ⇒ 42 - 7 ⇒ 35 cm. Hence, minimum length of the longest side of triangle = 35 cm. (iii) Minimum length of third side : Third side of triangle = 2x - 14 = 2(21) - 14 = 42 - 14 = 28 cm. Three sides of triangle = 21 cm, 28 cm and 35 cm. ⇒ 212 + 282 = 441 + 784 = 1225 ⇒ 352 = 1225. Thus, we can say that 212 + 282 = 352. Thus, it is a right angled triangle with hypotenuse 35 cm and other two sides are 21 cm and 28 cm. Hence, the triangle is right-angled triangle. (iv) By formula, Area of right angled triangle = × product of sides containing right angle Least area of the triangle = × 21 × 28 = 294 cm2. Hence, the least area of the triangle = 294 cm2.

Mathematics

Linear Inequations

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