Rectangle from diagonal and perimeter: The diagonal of a rectangle is 17 cm and its perimeter is 46 cm. Find the area (in sq. cm).

Introduction / Context:This problem combines Pythagoras with perimeter relations to determine a rectangle’s area from diagonal and perimeter.

Given Data / Assumptions:

• Sides a, b (cm).
• Diagonal d = 17 cm so a^2 + b^2 = 17^2 = 289.
• Perimeter P = 46 cm ⇒ a + b = 23.

Concept / Approach:Use identity (a + b)^2 = a^2 + b^2 + 2ab to find ab, which equals the area for rectangles.

Step-by-Step Solution:

Verification / Alternative check:If a = 8 and b = 15, then diagonal √(64+225)=√289=17 and perimeter 2*(8+15)=46; area 120 checks out.

Why Other Options Are Wrong:110, 130, 140 do not satisfy both the diagonal and perimeter constraints simultaneously.

Common Pitfalls:Trying to solve for individual a and b first; area can be obtained directly from the identity without explicit a, b values.

Final Answer:120