To explain: The perimeters of two rhombi having equal areas.
Answer to Problem 37HP
The perimeters of two rhombi having equal areas can be equal only when both rhombi are congruent.
Explanation of Solution
Given information: Areas of two rhombi are equal.
If the areas of two rhombi are equal. Then, the perimeters of two rhombi could be equal only when both rhombi are congruent. If both rhombi are not congruent, they have different length of sides.
Since, Area of rhombus = Base
So, base and height are the factors of the area. If the factors are different, the lengths of sides are different.
Thus, the perimeters of two rhombi having equal areas can be equal only when both rhombi are congruent.
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