The figure above shows the dimensions of an isosceles triangle in terms of x. What is the area of the triangle?
(A) 24
(B) 30
(C) 48
(D) 60
(E) 96
The OA is C.
Hi Swerve,
Let's take a look at your question.
Since the given triangle is an isosceles triangle, therefore, two of the sides of the triangle are congruent.
We can see that the base angles are the same i.e. y degrees, hence sides opposite to these two angles will be the same in length.
Therefore,
$$2x-2=3x-8$$
$$3x-2x=8-2$$
$$x=6$$
Now we can find the area of the triangle using the formula:
$$\text{Area of Triangle}=\frac{1}{2}\left(Base\right)\left(Height\right)$$
$$\text{Area of Triangle}=\frac{1}{2}\left(3x-2\right)\left(x\right)$$
Substitute x = 6, we get,
$$\text{Area of Triangle}=\frac{1}{2}\left[3\left(6\right)-2\right]\left(6\right)$$
$$\text{Area of Triangle}=\frac{1}{2}\left[18-2\right]\left(6\right)$$
$$\text{Area of Triangle}=\frac{1}{2}\left[16\right]\left(6\right)$$
$$\text{Area of Triangle}=8\left(6\right)=48$$
Therefore, Option
C is correct.
Hope it helps.
I am available if you'd like any follow up.
