Harrow School 13+ Maths Perimeter Question

In this video, Singapore Maths Academy walks through a classic algebraic perimeter question from a Harrow School 13+ entrance paper, where students must form and solve simultaneous equations based on geometric information.

We’re told:

• Rectangle 1 has length x cm, width y cm, and a perimeter of 73 cm.
• Rectangle 2 has a length of ⅓x and a width of 2y, with a perimeter of 36 cm.

The challenge is to form two equations using the perimeter formula and solve for x and y step by step. This type of question combines algebra, geometry, and problem translation — all key skills for high-performing students preparing for competitive senior school entry.

We guide students through writing the perimeter expressions for both rectangles, simplifying them, and solving the resulting simultaneous equations using substitution or elimination. It’s a perfect example of the applied algebraic thinking tested in the Harrow 13+ maths exam.