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The sum of the squares of the sides of a rhombus is 1600 cm2. What is the perimeter of the rhombus?
80 cm
40 cm
20 cm
60 cm
80 cm
Since all four sides of a rhombus are equal (a), the sum of squares is 4a². Given 4a² = 1600, find a² = 400, then a = 20. Perimeter is 4a = 4 * 20 = 80.
Sum of the squares of the sides of a rhombus = 1600 cm².
P=4a
Since all four sides of a rhombus are equal (a), the sum of squares is 4a². Given 4a² = 1600, find a² = 400, then a = 20. Perimeter is 4a = 4 * 20 = 80.
Confusing the 'sum of squares of sides' with 'sum of squares of diagonals' (Parallelogram Law), or forgetting that a rhombus has four equal sides.
Identify properties
A rhombus has four equal sides, each of length a. The sum of the squares of the sides is given as a2+a2+a2+a2=4a2.
4a2=1600
Calculate side length
Divide by 4 to find a2, then take the square root to find the side length a.
a2=41600=400⟹a=400=20 cm
Calculate perimeter
The perimeter of a rhombus is the sum of its four sides, calculated as P=4a.
P=4×20=80 cm
A is correct because the side length of the rhombus is 20 cm, making the perimeter 4 × 20 = 80 cm.
This concept of equal sides is fundamental in geometry; always check if a shape is a rhombus (all sides equal) or a rectangle (opposite sides equal) before applying perimeter formulas.
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