Applied Mathematics

Algebra

Easy

applied

The longest side of a triangle is 4 times the shortest side and the third side is 3 cm shorter than the longest side. If the perimeter of the triangle is at least 69 cm, then the minimum length of the shortest side is:

5 cm

6 cm

7 cm

8 cm

✅ Correct Option: 4

Let shortest side $= s$ . Longest $= 4s$ , third $= 4s - 3$ . Perimeter $= s + 4s + 4s - 3 = 9s - 3 \geq 69$ , giving $9s \geq 72$ , so $s \geq 8$ . Minimum shortest side $= 8$ cm.

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	A matrix which is both symmetric and skew symmetric	I.	symmetric matrix
B.	All positive integral powers of a symmetric matrix	II.	unit matrix
C.	Positive odd integral powers of a skew-symmetric matrix	III.	null matrix
D.	A square matrix $A = [a_{ij}]_{n\times n}$ with $a_{ij} = \begin{cases}0, & \forall\, i \neq j \\ 1, & \forall\, i = j\end{cases}$	IV.	skew-symmetric matrix

Choose the correct answer from the options given below:

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2023: 7 June Shift 1

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The longest side of a triangle is 4 times the shortest side and the third side is 3 cm shorter than the longest side. If the perimeter of the triangle is at least 69 cm, then the minimum length of the shortest side is:

Solution

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