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Triangles

Long Answer Type

391.

In the given Fig, DE || BC and DE divides ∆ABC in two parts such that ar (∆ADE) = $1 third area space increment ABC$ , prove that $space BD over AB equals fraction numerator square root of 3 minus 1 over denominator square root of 3 end fraction.$

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Short Answer Type

392. In the given fig. DE||BC and AD: DB = 3:4
Find (i)

fraction numerator area space left parenthesis increment DEF right parenthesis over denominator area thin space left parenthesis increment CFB right parenthesis end fraction

and (ii)

fraction numerator area left parenthesis increment ADE right parenthesis over denominator area left parenthesis increment ABC right parenthesis end fraction

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393. In ∆ABC, if AD is the median, show that AB² + AC² = 2 (AD² + BD²).

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394. ABCD is a square, F is the midpoint of AB and E is a point on BC such that BE is one-third of BC. If the area of ∆FBE is 108 cm², find the length AC.

Solution not provided.
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Long Answer Type

395. P is a point in the interior of rectangle ABCD. If P is joined to each of the vertices of the rectangle.
(A) Prove that PB² + PD² = PA² + PC².
(B) If PA, PB and PC are 3 cm, 4 cm and 5 cm respectively, find the length of PD.

1210 Views

396. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

114 Views