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Triangles

Short Answer Type

211. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

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212. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
(A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4.

∆ABC and ∆BDE are both equilateral triangles.
∴ ∆ABC ~ ∆BDE
[Using AAA similar condition].
We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.
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Hence, (c) 4 : 1 is the correct option.

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213.

Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio
(a) 2 : 3 (b) 4 : 9
(c) 81 : 16 (d) 16 : 81.

106 Views

Long Answer Type

214. Sides of some triangles are given below. Determine which of them are right triangles. In case of a right angle, write the length of its hypotenuse.
(i) 7 cm, 24 cm, 25 cm
(ii) 3 cm, 8 cm, 6 cm
(iii) 50 cm, 80 cm, 100 cm
(iv) 13 cm, 12 cm, 5 cm.

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215. PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR show that PM² = QM × MR.

283 Views

216.

In the given fig, ABD is a triangle right angled at A and AC ⊥ BD. Show that
(i) AB² = BC .BD
(ii) AC² = BC. DC
(iii) AD² = BD . CD

214 Views

Short Answer Type

217. ABC is an isosceles triangle right angled at C. Prove that AB² = 2AC².

233 Views

218. ABC is an isosceles triangle with AC = BC. If AB² = 2AC², prove that ∆ABC is a right triangle.

844 Views

Long Answer Type

219. ABC is an equilateral triangle of side 2a. Find each of its altitudes.

397 Views

220. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

198 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

212. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is(A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4.

Long Answer Type

Short Answer Type

Long Answer Type

212. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
(A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4.