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vinay kumar

· started a discussion

· 1 Months ago

concept used (Question: 223896.0 )

what is the concept used?

Question:

ABCD is trapezium in which AD||BC. AB = 9 cm, BC = 12 cm, CD = 15 cm, DA = 20 cm. Find the sum of square of diagonals.  

Options:
A) 686
B) 720
C) 786
D) 700
Solution:
Ans: (c) Sum of square of diagonals 

= 92 + 152 + 2 × 20 × 12

= 81 + 225 + 480

= 786

Knowledge Expert

· commented

· 1 Months ago

Dear Student,

Let the height be h. Base be 20 top be 12.

Draw perpdiculars from the edges of the top to the base.

We have left overs of the base on both the sides. call them x and y.

Now X+Y =8 ( hope u got)

Now sum of the diagonals is nothing but h^2 + (20-y)^2 + h^2 + (20-x)^2

it comes out to be 800-40(x+y)+2 h^2 + X^2 + Y^2

We have h^2+X^2 = 9^2 and h^2+ Y^2 = 15^2 and X + Y = 8

Ans = 786


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