Answer:
x = 14.4
Step-by-step explanation:
Similar means that the figures are proportional to each other. Because of this, we can form a problem. (the short side lengths) =
(the long side lengths). Now we can solve this by cross-multiplying. If we multiply 9 · 8 we get 72, and 5 · x is 5x. 72 = 5x. Now divide both sides by 5. 72 ÷ 5 = 14.4. Therefore, x should be equal to 14.4. Does this make sense?
Given:
The three lengths in the options.
To find:
Which three lengths could be the lengths of the sides of a triangle?
Solution:
If the sum of two smaller sides is greater than the largest side, then the three sides can form a triangle otherwise the triangle is not possible.
In option A, the three sides are 4 cm, 8 cm, 13 cm. Here, the largest side is 13 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
In option B, the three sides are 13 cm, 11 cm, 23 cm. Here, the largest side is 23 cm.
Sum of two smaller sides is:
So, the triangle is possible.
In option C, the three sides are 5 cm, 18 cm, 12 cm. Here, the largest side is 18 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
In option D, the three sides are 25 cm, 8 cm, 16 cm. Here, the largest side is 25 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
Therefore, the correct option is B. The three lengths 13 cm, 11 cm, 23 cm could be the lengths of the sides of a triangle.