Which three lengths could be the lengths
1 answer:
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.
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Answer: The answers is (B) equal areas.
Step-by-step explanation: Given that two triangles have equal perimeters.
As shown in the attached figure, let us consider two right-angles triangles, ΔABC and ΔDEF, with sides AB = 3 cm, BC = 4 cm, AC = 5 cm, DE = 4 cm, EF = 3 cm and DF = 5 cm.
So the perimeters of both the triangles = 3 + 4 + 5 = 4 + 3 + 5 = 12 cm.
Since volume term is not valid in case of triangles, so they cannot have equal volumes. Therefore, option (A) is incorrect.
Area of ΔABC is
and area of ΔDEF is
Therefore, they may have equal areas and so option (B) is correct.
If the triangles have equal bases, then the heights will also be equal and both the triangles will be same. Similar is the case with equal heights. So, options (C) and (D) are incorrect.
Thus, the correct option is (B). equal areas.
