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A triangular sign board is isosceles. If the unequal side is 7 cm and one of the equal sides is 6 cm, what is the measure of the third side?
- a)5cm
- b)6cm
- c)7cm
- d)Either [a] or [c]
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A triangular sign board is isosceles. If the unequal side is 7 cm and ...
(B) is the correct answer because in isosceles triangle the two sides are equal and one side is unequal.
Here, one unequal side is =7
So, two equal sides are =6
Here, one unequal side is =7
So, two equal sides are =6
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Community Answer
A triangular sign board is isosceles. If the unequal side is 7 cm and ...
Given Information:
- An isosceles triangular sign board.
- One side is unequal and measures 7 cm.
- One side is equal to 6 cm.
Solution:
To find the measure of the third side, we need to determine whether it is equal to 5 cm or 7 cm.
Isosceles Triangle:
An isosceles triangle is a triangle that has two sides of equal length. In this case, the given sign board is an isosceles triangle.
Properties of an Isosceles Triangle:
- The base angles of an isosceles triangle are equal.
- The side opposite the base angle is also equal in length to the other two sides.
Given Side Lengths:
- Unequal side: 7 cm
- Equal side: 6 cm
Base Angle:
Let's assume the unequal side is the base of the triangle. Therefore, the base angle would be the angle opposite to the unequal side.
Using the Base Angle:
Since the triangle is isosceles, the base angle can be used to determine the measure of the third side.
Case 1: Third Side = 5 cm
If the third side is 5 cm, then the base angle would be larger than the angle formed by the two equal sides.
Case 2: Third Side = 7 cm
If the third side is 7 cm, then the base angle would be smaller than the angle formed by the two equal sides.
Conclusion:
Since the base angle of an isosceles triangle cannot be larger than the angle formed by the two equal sides, we can conclude that the measure of the third side is 7 cm, not 5 cm.
Correct Answer:
The measure of the third side is 7 cm, therefore the correct answer is option 'B': 6 cm.
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A triangular sign board is isosceles. If the unequal side is 7 cm and one of the equal sides is 6 cm, what is the measure of the third side?a)5cmb)6cmc)7cmd)Either [a] or [c]Correct answer is option 'B'. Can you explain this answer?
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