MAT Exam 2025 Paper

Concept:Use the area formula of a right triangle and factorization to find the two perpendicular sides, then apply Pythagoras theorem.Explanation:Let the shorter side be $x$ cm and the longer side be $(x+23)$ cm.Area of right triangle = $\frac{1}{2} \times \text{base} \times \text{height}$.So, $\frac{1}{2} \times x \times (x+23) = 210$.This gives $x(x+23) = 420$.Thus, $x^2 + 23x - 420 = 0$.Factorizing: $(x - 12)(x + 35) = 0$.So, $x = 12$ cm, since $x = -35$ is not possible.Hence, the two sides are $12$ cm and $35$ cm.Using Pythagoras theorem: $H^2 = 12^2 + 35^2 = 144 + 1225 = 1369$.Therefore, $H = 37$ cm.Perimeter $= 12 + 35 + 37 = 84$ cm.Answer:$84$ cm, i.e., Option A.