Question

find the missing side length.
assume that all intersecting sides meet at right angles.
include the correct unit in your answer

diagram of a composite rectangle with labeled sides: 15 cm, 4 cm, 8 cm, 5 cm, 7 cm

input box unit options: cm, m, km buttons: refresh, close

Explanation:

Step1: Analyze vertical sides

The vertical side on the left is 4 cm, and there's a 5 cm segment. Let the missing vertical side be \( y \). The total vertical length should match the sum of these. Wait, actually, for the horizontal and vertical sides, in a right-angled composite figure, the sum of the horizontal segments on the bottom should equal the top, and vertical segments on the right equal the left. Wait, let's look at vertical: the left has 4 cm, then a 5 cm? Wait, no, the figure: top length 15 cm, left side 4 cm, then a horizontal 8 cm, vertical 5 cm, and bottom right 7 cm. Wait, vertical sides: the leftmost vertical is 4 cm, then there's a 5 cm vertical segment (downward?), and the total vertical height (the missing side, let's call it \( h \)) should be \( 4 + 5 = 9 \) cm? Wait, no, maybe horizontal: the top is 15 cm. The bottom has 8 cm and 7 cm? Wait, 8 + 7 = 15, which matches. Now vertical: the left side is 4 cm, and there's a 5 cm segment. So the right vertical side (the missing one) should be \( 4 + 5 = 9 \) cm. Let's check: vertical segments: 4 cm (up) and 5 cm (up), so total height is 4 + 5 = 9 cm.

Step2: Calculate missing side

So the missing side length is \( 4 + 5 = 9 \) cm.

Answer:

9 cm