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Maths-

General

Easy

Question

In △ 𝑅𝑆𝑇, which is a possible side length for ST?

7
8
9
Cannot be determined

hint Hint:

Sum of angles of triangle is 180o.

In triangle, the side opposite to largest angle is largest.

In triangle, the side opposite to smallest angle is shortest.

The correct answer is: 9

Step by step explanation:

Given:

∠RST = 65^o
∠STR = 56^o

Step 1: Find ∠SRT

Sum of angles of triangle is 180^o.
∠RST + ∠STR + ∠SRT = 180^o
65 + 56 + ∠SRT = 180
121 + ∠SRT = 180
∠SRT = 180 - 121
∠SRT = 59^o

Step 2: In △RST,

∠SRT > ∠STR
the side opposite to largest angle is largest
ST > SR
ST > 8
Hence, possible length of ST may be more than 8.

Final Answer:

Correct option C. 9

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