Maths · Geometry · chapter 6 of 14
Class 10 Maths Chapter 6: Triangles case study question with answers
One case-based question of the kind the board asks in Section E: a passage and a figure, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
Students of a school near the Narmada want the width of the river without crossing it. They pick a tree T on the far bank and stand at A on the near bank, directly opposite T, so that TA is perpendicular to the bank. They walk 20 m along the bank to a point B and fix a peg. Back at A, they walk 8 m straight away from the river, along TA produced, to a point D. From D they walk parallel to the bank until, at E, the peg B and the tree T are in one line with E. DE measures 25 m, as in the figure.
Part 1 · 1 mark
ΔTAB and ΔTDE are similar by the criterion
Show answer
Answer: (b) AA
∠T is common and ∠TAB = ∠TDE = 90° (AB ∥ DE), so two pairs of angles are equal.
Part 2 · 1 mark
From the similarity, TATD is equal to
Show answer
Answer: (a) ABDE
T ↔ T, A ↔ D, B ↔ E, so TA/TD = AB/DE = TB/TE.
Part 3 · 2 marks
Find the width TA of the river.
Answer and marking scheme
Let TA = x m. Then TD = x + 8. x/(x + 8) = 20/25, so 25x = 20x + 160 and x = 32 m.
- x/(x + 8) = 20/25 (1)
- TA = 32 m (1)
Or
On another day the group keeps AB = 20 m and AD = 8 m but finds DE = 30 m at a different spot. Find the width TA there.
Answer and marking scheme
x/(x + 8) = 20/30, so 30x = 20x + 160 and x = 16 m.
- x/(x + 8) = 20/30 (1)
- TA = 16 m (1)
← Chapter 5: Arithmetic ProgressionsChapter 7: Coordinate Geometry →