Question

The diagonal of a rectangle is 347 millimeters, while the longer side is 275 millimeters. Find the shorter side of the rectangle. (Round your answer to the nearest whole number.)

A) 208 mm
B) 208.72 mm
C) 209 mm
D) 209.12 mm

Answer 1

Using the Pythagorean theorem, the length of the shorter side of the rectangle is calculated to be approximately 208.72 mm. When rounded to the nearest whole number, the answer is 209 mm, aligning with Option C.

Step-by-step explanation:

The correct answer is option B) 208.72 mm, which we find by using the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. For a rectangle, the diagonal acts as the hypotenuse, and the sides of the rectangle are the other two sides of the triangle.

To find the length of the shorter side, we calculate:

1. 347 mm2 = 275 mm2 + shorter side2
2. shorter side2 = 347 mm2 - 275 mm2
3. shorter side2 = 120409 mm2 - 75625 mm2
4. shorter side2 = 44784 mm2
5. shorter side = √44784 mm2
6. shorter side ≈ 208.72 mm (rounded to two decimal places)

Since the question asks to round off to the nearest whole number, the answer is approximately 209 mm (Option C), but when specifically asking for two decimal places, the more precise answer is 208.72 mm (Option B).