The problem states that the area of the triangle is $35 cm^2$. We need to find the value of $y$.

GeometryAreaTriangleAlgebraic Equations
2025/7/16

1. Problem Description

The problem states that the area of the triangle is 35cm235 cm^2. We need to find the value of yy.

2. Solution Steps

Let's denote the base of the triangle as bb and the height as hh.
The area of a triangle is given by:
Area=12×base×heightArea = \frac{1}{2} \times base \times height
The base of the triangle is 3+y3+y, and the height is 77. We are given that the area is 35cm235 cm^2.
Therefore, we can write the equation:
35=12×(3+y)×735 = \frac{1}{2} \times (3+y) \times 7
Multiply both sides by 2:
70=(3+y)×770 = (3+y) \times 7
Divide both sides by 7:
10=3+y10 = 3+y
Subtract 3 from both sides:
y=103y = 10-3
y=7y = 7
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:
Area=12×base×heightArea = \frac{1}{2} \times base \times height
35=12×(3+y)×735 = \frac{1}{2} \times (3+y) \times 7
70=7(3+y)70 = 7(3+y)
10=3+y10 = 3+y
y=7y = 7
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 = 35cm235cm^2.
(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 28cm228cm^2, which leads to the solution:
28=0.5(3+y)728 = 0.5 * (3+y) * 7
56=(3+y)756 = (3+y) * 7
8=3+y8 = 3+y
y=5y = 5.
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:
35=0.5(3+y)535 = 0.5 * (3+y) * 5
70=(3+y)570 = (3+y) * 5
14=3+y14 = 3+y
y=11y = 11.
With none of the answers making sense, I am going to re-check the original problem, assuming I did not miss anything.
Area = 12×base×height\frac{1}{2} \times base \times height
35=12×(3+y)×735 = \frac{1}{2} \times (3+y) \times 7
Multiply both sides by 2:
70=(3+y)×770 = (3+y) \times 7
Divide both sides by 7:
10=3+y10 = 3+y
Subtract 3 from both sides:
y=7y = 7

3. Final Answer

None of the given options are correct. The value of y is 7.

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