Given that
rac{4x-y}{3y} = \frac{1}{2}" alt="\frac{4x-y}{3y} = \frac{1}{2}" align="absmiddle" class="latex-formula"> , find the value of 
1 answer:
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Given:
The three lengths in the options.
To find:
Which three lengths could be the lengths of the sides of a triangle?
Solution:
If the sum of two smaller sides is greater than the largest side, then the three sides can form a triangle otherwise the triangle is not possible.
In option A, the three sides are 4 cm, 8 cm, 13 cm. Here, the largest side is 13 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
In option B, the three sides are 13 cm, 11 cm, 23 cm. Here, the largest side is 23 cm.
Sum of two smaller sides is:
So, the triangle is possible.
In option C, the three sides are 5 cm, 18 cm, 12 cm. Here, the largest side is 18 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
In option D, the three sides are 25 cm, 8 cm, 16 cm. Here, the largest side is 25 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
Therefore, the correct option is B. The three lengths 13 cm, 11 cm, 23 cm could be the lengths of the sides of a triangle.
Answer:
△ABC and △DEF are similar by SAS Similarity Theorem.
Option (C) is correct .
Step-by-step explanation:
Definition of SAS Similarity property
Two triangles are said to be similar by SAS Similarity property If two sides are proportional and one corresponding angle congruent .
In △ABC and △DEF
and
Thus
∠ABC = ∠DEF (As given in the figure )
Thus △ABC and △DEF are similar by SAS Similarity property .