A rectangle, one side of which is 2 cm larger than the other, has an area equal to the area of a square
September 25, 2021 | education
| A rectangle, one side of which is 2 cm larger than the other, has an area equal to the area of a square with a side 4 cm less than the perimeter of the rectangle. Find the sides of the rectangle.
1. Sides of rectangle a and b:
b = a + 2.
2. Perimeter of the rectangle:
P = 2 (a + b) = 2 (a + a + 2) = 2 (2a + 2) = 4 (a + 1).
3. Area of the rectangle:
S1 = ab = a (a + 2).
4. Side of the square:
x = P – 4 = 4 (a + 1) – 4 = 4a + 4 – 4 = 4a.
5. Square area:
S2 = x ^ 2 = (4a) ^ 2 = 16a ^ 2.
6. The areas of a rectangle and a square are equal:
S1 = S2;
a (a + 2) = 16a ^ 2;
a ^ 2 + 2a = 16a ^ 2;
15a ^ 2 – 2a = 0;
a (15a – 2) = 0;
15a – 2 = 0;
15a = 2;
a = 2/15;
b = a + 2 = 2/15 + 2 = 32/15.
Answer: 2/15 cm and 32/15 cm.
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