Aboard an orbital station, Nova and Luna needed to replace a damaged rectangular satellite panel measuring 6 meters by 4 meters. Their supply room contained only 24 square meters of material, so they could not afford any waste. One design used rectangular sections, while another divided the panel into right triangles with legs of 3 meters and 4 meters. Luna calculated that each triangle had an area of 6 square meters, so four triangles would cover exactly 24 square meters. Nova checked the angles and side lengths. Two matching right triangles could be joined along their 5-meter sides to form a 3-meter by 4-meter rectangle, and two such rectangles would fit together to cover the damaged 6-meter by 4-meter region without gaps. Since the triangular design used exactly the available material and formed the required shape, they selected it. The replacement fit perfectly, and the satellite was ready to return to service.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Use one-half times base times height for each triangle, then compare the total with 6 times 4.
Why do four right triangles with legs of 3 meters and 4 meters use exactly enough material to cover the 6-meter by 4-meter satellite panel?
Each triangle has area 12 square meters, and four triangles have area 48 square meters.Each triangle has area 6 square meters, and four triangles have area 24 square meters, equal to the panel's area.Each triangle has area 7 square meters, and four triangles have area 28 square meters.Each triangle has area 5 square meters, and four triangles have area 20 square meters.
Correct. Four triangles each covering 6 square meters have the same total area as the 24-square-meter panel.
Find the area of one right triangle first, multiply by four, and compare the result with the panel's area.
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Hint
Square the two leg lengths, add the results, and find the positive square root.
Nova wants to verify the side along which two matching triangles are joined. Each right triangle has legs of 3 meters and 4 meters. Using the Pythagorean theorem, what is the length in meters of the hypotenuse?
Correct. The hypotenuse of a right triangle with legs 3 and 4 meters is 5 meters.
Use the Pythagorean theorem with 3 and 4 as the two leg lengths.
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Hint
Two matching right triangles can form a rectangle whose side lengths match the triangle's legs. Then consider what two of those rectangles can form.
Nova and Luna join two matching 3-meter by 4-meter right triangles along their 5-meter hypotenuses. Which statement correctly describes the resulting shape and explains how the four triangles can cover the panel?
Two triangles form a 3-meter by 4-meter rectangle; two such rectangles have a total area of 24 square meters and can be arranged to form the 6-meter by 4-meter panel.Two triangles form a 5-meter by 5-meter square; two such squares have a total area of 50 square meters.Two triangles form a 3-meter by 4-meter rectangle; one such rectangle alone covers the entire 6-meter by 4-meter panel.Four triangles form a 3-meter by 4-meter rectangle with a total area of 12 square meters.
Correct. Each pair forms a 3-meter by 4-meter rectangle, and two such rectangles can make the required 6-meter by 4-meter panel.
Use the 3-meter and 4-meter legs to determine the rectangle formed by each pair of triangles, then combine two rectangles.
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Uydu Paneli Tasarımı
TR
ARC_G10_GM_02_STORY_01
Uydu Paneli Tasarımı
The Satellite Panel Design
EN
ARC_G10_GM_02_STORY_01
The Satellite Panel Design