Suppose the base of a triangle expands by 25% while its height contracts by 12%. Determine the net percentage change in its area.

The correct option is 10%.

Step 1: Formula for the area of a triangle.
The area ($A$) of a triangle is given by:

$A=\frac{1}{2}\times b\times h$

where $b$ is the initial base length and $h$ is the initial height of the triangle.

Step 2: Calculate the modified base and height.
When the base expands by 25%, the new base ($b_{\text{new}}$) becomes:

$b_{\text{new}}=b+0.25b=1.25b$

When the height contracts by 12%, the new height ($h_{\text{new}}$) becomes:

$h_{\text{new}}=h-0.12h=0.88h$

Step 3: Calculate the new area.
Substituting $b_{\text{new}}$ and $h_{\text{new}}$ into the area formula gives the new area ($A_{\text{new}}$):

$A_{\text{new}}=\frac{1}{2}\times b_{\text{new}}\times h_{\text{new}}$

$A_{\text{new}}=\frac{1}{2}\times (1.25b)\times (0.88h)$

$A_{\text{new}}=(1.25\times 0.88)\times \left(\frac{1}{2}\times b\times h\right)$

$A_{\text{new}}=1.10\times A$

Step 4: Find the net percentage change in area.
The net percentage change is:

$\text{Percentage Change}=\frac{A_{\text{new}}-A}{A}\times 100\%$

$\text{Percentage Change}=\frac{1.10A-A}{A}\times 100\%$

$\text{Percentage Change}=0.10\times 100\%=10\%$

Therefore, the area of the triangle increases by 10%.