Statement 1- In an equilateral triangle- the heights onto all the sides are equal- Statement 2- The base lengths are also equal in an equilateral triangle- Statement 1 is correct but statement 2 is incorrect-Statement 1 is incorrect but statement 2 is correct-Both the statements are correct-Both the statements are incorrect-

The correct option is C Both the statements are correct Area of a triangle = 1/2×base×height, All the base lengths (sides) are equal in an equilateral triangle ...

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Standard VIII

Mathematics

Area of Special Triangles

Statement 1: ...

Question

Statement 1: In an equilateral triangle, the heights onto all the sides are equal.
Statement 2: The base lengths are also equal in an equilateral triangle.

True

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False

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Both the statements are correct

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Both the statements are incorrect

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Solution

The correct option is C
Both the statements are correct

$Area of a triangle$ = $\frac{1}{2} \times base \times height$ ,
All the base lengths (sides) are equal in an equilateral triangle.
Since the area is also same, the heights should be the same.

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Similar questions

Statement 1: In an equilateral triangle, the heights onto all the sides are equal.
Statement 2: The base lengths are also equal in an equilateral triangle.

Statement 1: If two figures A and B are congruent, then they must have equal area.

Statement 2: If two figures A and B have equal area, then they must be congruent.

Statement 1: In the figure areas of both parallelogram ABCD and the triangle ABE are equal.

Statement 2: Both the triangle and parallelogram have same base and height.

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Statement 1: In an equilateral triangle, the heights onto all the sides are equal. Statement 2: The base lengths are also equal in an equilateral triangle.

The correct option is C Both the statements are correct Area of a triangle = 12×base×height, All the base lengths (sides) are equal in an equilateral triangle. Since the area is also same, the heights should be the same.

Statement 1: In an equilateral triangle, the heights onto all the sides are equal.
Statement 2: The base lengths are also equal in an equilateral triangle.

The correct option is C
Both the statements are correct

$Area of a triangle$ = $\frac{1}{2} \times base \times height$ ,
All the base lengths (sides) are equal in an equilateral triangle.
Since the area is also same, the heights should be the same.