Perimeter & Area

Problem

Distance between parallel sides equals the side length

Three squares A, B, C are lined up left to right with their bottoms aligned. The left side of A (segment GH) is 9 cm tall. A's top is 2 cm higher than B's top, and B's top is 2 cm higher than C's top. I need the horizontal distance between segment GH (left side of A) and segment KJ (right side of C).
9 cm 2 cm 2 cm A B C G H K J
GeometryMeasurement & data
Your answer
cm
How to solve
Strategy Identify Subproblems — Since the bottoms are aligned, the height difference between two adjacent square tops equals the difference of their side lengths. I first find each square's side as a small subproblem, then add the three sides because GH and KJ are the two outer vertical sides, so the gap between them is just the total width of the row.
1STEP 1

Side of square A

Square A's left side GH is given as 9 cm, and a square has all sides equal, so A's side length is 9 cm.

a = 9 cm
2STEP 2

Side of square B

Bottoms align, so the 2 cm top gap is how much shorter B's side is than A's: 9 - 2 = 7 cm.

b = 9 - 2 = 7 cm
3STEP 3

Side of square C

B's top is 2 cm higher than C's top, so C's side is 2 cm shorter than B's: 7 - 2 = 5 cm.

c = 7 - 2 = 5 cm
4STEP 4

Add the three widths

GH and KJ are the far-left and far-right vertical sides, so the gap between them is the whole row: 9 + 7 + 5 = 21 cm.

9 + 7 + 5 = 21 cm
Answer
21 cm
9 + 7 + 5 = 21 cm
The three sides are 9, 7, and 5 cm, each a sensible square size, and 9 + 7 + 5 = 21 cm. The answer is larger than any single square width, which is right because GH and KJ sit at opposite ends of all three squares.
Takeaway

Lined-up squares: the step between their tops is the difference of their sides, so you just add the widths!

  • Side of square A
  • Side of square B
  • Side of square C
  • Add the three widths
Where next?
Another one like thissuggested

▶ Practice — 10 problems