Think You’re Good at Geometry? Try This One
7.1K views · Sep 22, 2026 · Education
Comments · 20
@CipriValdezate · 5 days ago (edited)
Easier: By the Thales theorem, the length of the rectangle has 3 measures: 3x + 15x + 2x, and the height 15x, then (20x)² + (15x)² = 20², then x = 4 / 5, then the side of the square is 15x = 12 and the area of the square 144.
1
@humbertorios2941 · 8 days ago
Eu gostei mais da segunda solução. Bem simples.
@pperry · 6 days ago
Si on fait glisser le carré vers la gauche ou vers la droite, on élimine un des 2 petits triangles et le problème est plus simple car il n’y a plus que 2 triangles semblables. On applique Thales .
2
@johnallen3555 · 4 days ago (edited)
1 Call the Angle of line PU with respect to line PR = A radians (or degrees, or even grad if you wish)<br>2 The vertical side of the square is L= (2+15+3)sin (A) = 20Sin (A)<br>3 The Horoz side of the square = L = 15cos (A)<br>4 Thus 15cos(A) = 20sin(A) <br>5 rearranging 20 sin (A) -15cos(A) = zero must be true for the area of interest to be a square<br>6 Solving [eqn 5] =0 gives the angle at which the closed section becomes a square = 0.64 radians 36.84 deg. This solving can be done numerically or with some more algebra or old school drawing a graph of the function if ones alegbra is hard work for you<br>7 Now substuting this into eqn 2 gives L = 20sin (0.64radian) = 12<br>8 Thus the Area of the square is 12x12 = 144
1
@TimVy-r9c · 7 days ago
Good stuff 👍👍
1
@benv6875 · 8 days ago
It's a 3,4,5 triangle, side length is 12 , Area = 144,
1
@tuannguyendinh4321 · 8 days ago
Translate the line segment PU to the right so that P coincides with Q and point U moves to position V. Then QV = 20, QT = t, and TV/TS = 20/15 = 4/3.<br>=> TV = (4/3)TS = 4t/3<br>QT^2 + TV^2 = QV^2<br><=> t^2 + (4t/3)^2 = 20^2<br><=> 25t^2/9 = 400 <=> t^2 = 144<br>=> Area = t^2 = 144
1
@משהנאון-י6מ · 6 days ago
S=100
1
@sanjeevkumarpamu2206 · 8 days ago
Madam! Who suggested that formula. Tell me please 😊😊😊
@sakurayayoi-p2r · 6 days ago
ＰＵを水平移動しＰをＱにかさねると15と５に分かれる。Ｕ’、ＳＲとＱｕ’の交点をＨとする。ＳＨ＝ｓ、Ｕ’Ｓ＝Ｐとし、三角形の相似から５：２０＝s:ｔ、４ｓ＝ｔ。ｔ＋ｐ：ｐ＝４：１、ｔ＝３ｐ。三平方でｓｓ＋ｐｐ＝25。ｓ＝３／４ｐを代入しｐ＝4。ｔ＝12。ｔｔ＝144。
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