Question

We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?

A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated

Answer 1

Explanation:

Let's start by calculating the area of each square. We can do this by squaring the length of one of the sides. If we assume that both squares have the same length, we can call this length "x".

The area of the first square would then be x^2, and the area shaded would be 2/12 of this. Simplifying this fraction, we get 1/6. So the shaded area of the first square is (1/6)x^2.

The area of the second square is also x^2, and the shaded area is 2/15 of this. Simplifying this fraction, we get 2/15. So the shaded area of the second square is (2/15)x^2.

To find the total shaded area, we simply add these two areas together:

(1/6)x^2 + (2/15)x^2

To simplify this expression, we can find a common denominator for the fractions:

(5/30)x^2 + (4/30)x^2

Combining the terms, we get:

(9/30)x^2

Simplifying the fraction, we get:

(3/10)x^2

So the total shaded area is (3/10)x^2.

To find the fraction of the total diagram that is shaded, we need to divide this by the total area of the diagram, which is the sum of the areas of the two squares:

x^2 + x^2 = 2x^2

Dividing the shaded area by the total area, we get:

(3/10)x^2 / 2x^2 = 3/20

So the fraction of the total diagram that is shaded is 3/20.

In summary, we calculated the area of each square, found the shaded area of each square, added these together to get the total shaded area, and then divided this by the total area of the diagram to find the fraction that is shaded. The answer is 3/20. which is approximately equal to 0.148 repeated.

Answer 2

Explanation:

To solve this problem, we need to find the total shaded area and then divide it by the total area of the diagram.

Let's first find the area of each square. Since the area of a square is given by the formula A = s^2, where s is the length of a side, we can find the length of a side by taking the square root of the area.

For the first square, the shaded area is 2/12, or 1/6, of the total area. So, if we let x be the length of a side, we have:

(1/6)x^2 = 2/12

Simplifying, we get:

x^2 = 2/12 * 6

x^2 = 1

x = 1 (since the length of a side cannot be negative)

So, the first square has an area of 1 square unit.

For the second square, the shaded area is 2/15 of the total area. So, if we let y be the length of a side, we have:

(2/15)y^2 = 2/12

Simplifying, we get:

y^2 = (2/15) * (12/2)

y^2 = 1.6

y = 1.2649 (rounded to four decimal places)

So, the second square has an area of approximately 1.6 square units.

To find the total shaded area, we add the shaded areas of the two squares:

1/6 + 2/15 = 5/30 + 4/30 = 9/30 = 3/10

To find the total area of the diagram, we add the areas of the two squares:

1 + 1.6 = 2.6

Finally, we divide the total shaded area by the total area of the diagram:

3/10 ÷ 2.6 ≈ 0.1154

Therefore, the answer is not one of the choices given. The closest answer is A. 0.148, but the correct answer is actually slightly less than that.