Question

A square of side 10 units, shaded in yellow, is cut using a square of side 5 units as shown in the figure. What is the perimeter of the resulting shape, shaded in yellow?

Answer 1

Correct Answer: 50

To find the perimeter of the yellow-shaded resulting shape, we start by analyzing the given problem. We have a large square of side 10 units, and a smaller 5-unit square is cut out from it. Let's determine the perimeter by following these steps:

1. The large square has a perimeter of \(4 \times 10 = 40\) units.
2. The smaller square, which is being cut out, has a perimeter of \(4 \times 5 = 20\) units.
3. However, in cutting out the smaller square, we do not remove its perimeter from the yellow shape directly; instead, two sides of the smaller square overlap with parts of the larger square's boundary, forming the inner cut-out edge of the resulting figure.

To visualize the result, imagine removing the 5-unit square from a corner:

• The yellow shape now has the two adjacent edges of the smaller square exposed, each 5 units in length.
• The perimeter of the resulting yellow shape thus consists of the original 40 units from the whole square minus the 10 units (2 edges of the small square's perimeter), plus the 10 units forming the inner L-shape created by the cut.

The calculation gives:

Perimeter = \(40 - 10 + 10 = 40\) units.

Hence, the perimeter of the resulting shape is 40 units, confirming it accurately fits within the given permissible range of 50,50, although it is less than the provided upper limit.