The problem states that the area of the triangle is $35 cm^2$. We need to find the value of $y$.
2025/7/16
1. Problem Description
The problem states that the area of the triangle is . We need to find the value of .
2. Solution Steps
Let's denote the base of the triangle as and the height as .
The area of a triangle is given by:
The base of the triangle is , and the height is . We are given that the area is .
Therefore, we can write the equation:
Multiply both sides by 2:
Divide both sides by 7:
Subtract 3 from both sides:
However, none of the given options match this answer. Let's re-examine the problem setup and perform error checking. The height and base seem to be correctly identified. Let's solve again:
Since 7 is not an option, let's assume that the area given is incorrect and go through the options to see if they make sense with the area = .
(a) if y = 5, Area = 0.5 * (3+5) * 7 = 0.5 * 8 * 7 =
2
8. (Incorrect)
(b) if y = 10, Area = 0.5 * (3+10) * 7 = 0.5 * 13 * 7 = 45.5 (Incorrect)
(c) if y = 15, Area = 0.5 * (3+15) * 7 = 0.5 * 18 * 7 = 63 (Incorrect)
(d) if y = 20, Area = 0.5 * (3+20) * 7 = 0.5 * 23 * 7 = 80.5 (Incorrect)
It is highly unlikely that there is some typo in the question, and it might be reasonable to assume that the area is actually , which leads to the solution:
.
If this is the case, (a) might be the solution. However, based on the problem stated, it does not seem that the option matches.
The only viable solution will be that y = 7 if the problem is defined to be correct.
If the question wanted an integer solution to be matched by choice (b), consider changing the height to 5 such that:
.
With none of the answers making sense, I am going to re-check the original problem, assuming I did not miss anything.
Area =
Multiply both sides by 2:
Divide both sides by 7:
Subtract 3 from both sides:
3. Final Answer
None of the given options are correct. The value of y is 7.