30 August, 16:39

# The longer side of a rectangle is 3 times the length of the shorter side. If the diagonal of the rectangle is 10cm what are the dimensions of the rectangle?

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1. 30 August, 17:12
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Answer: I think it might be 30 because 10*3.
2. 30 August, 18:33
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Answer: the shorter side is 3.16 cm

The longer side is 9.48 cm

Step-by-step explanation:

The diagonal of the rectangular garden divides it into two equal right angle triangles. The diagonal represents the hypotenuse of each right angle triangle. The shorter and longer sides of the rectangle represents the adjacent and opposite sides of the right angle triangle.

Let w represent the shorter side of the triangle. The longer side of a rectangle is 3 times the length of the shorter side. It means that length of the longer side is 3w

Since the diagonal of the rectangle is 10cm, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore

10² = (3w) ² + w²

100 = 9w² + w² = 10w²

w² = 100/10 = 10

w = √10 = 3.16 cm

The longer is 3 * 3.16 = 9.48 cm