JAMIA 2026 — Mathematics PYQ

Step 1: Formula for the area of a triangle

The standard formula to calculate the area ($A$) of a right-angled triangle with base ($b$) and height ($h$) is:

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

Step 2: Set up the conditions for the new triangle

Let the initial parameters of the triangle be:

• Initial Base = $b$

• Initial Height = $h$

• Initial Area = $A_1=\frac{1}{2}bh$

According to the question, the new parameters are modified as follows:

• New Base ($b^{\prime }$) = $2b$ (since it is doubled)

• New Height = $h^{\prime }$

• New Area = $A_2$

Step 3: Equate the initial area to the new area

The problem states that the total area must remain unchanged, which mathematically means $A_2=A_1$:

$$\frac{1}{2}\times b^{\prime }\times h^{\prime }=\frac{1}{2}\times b\times h$$

Substitute $b^{\prime }=2b$ into the equation:

$$\frac{1}{2}\times (2b)\times h^{\prime }=\frac{1}{2}\times b\times h$$

Step 4: Solve for the new height ($h^{\prime }$)

Cancel out the common term $\frac{1}{2}$ from both sides:

$$2b\times h^{\prime }=b\times h$$

Now, divide both sides by $b$ (assuming $b\ne 0$):

$$2h^{\prime }=h$$

$$h^{\prime }=\frac{1}{2}h$$

Conclusion:

To keep the area constant when the base is doubled, the height must be multiplied by a factor of $\frac{1}{2}$ (i.e., it must be halved).

Correct Answer

The correct option is (a) $1/2$.