Question

Let ABCD be a convex quadrilateral with perpen-
dicular diagonals. If AB = 20, BC = 70 and CD = 90,
then what is the value of DA ?​

Answer 1

The value of DA is 60cm

GIVEN

ABCD is a convex quadrilateral.

Diagonals are perpendicular to each other

AB = 20cm

BC = 70 Cm

CD = 90cm

TO FIND

The value of DA.

SOLUTION

We can simply solve the above problem as follows -

It is given,

ABCD is a convex quadrilateral.

since, AC ⊥ BD

So,

The sum of square two opposite sides is equal to the square of the sum of other two sides

${AB}^{2} + {CD}^{2} = {BC}^{2} + {DA}^{2}$

Putting the values in the above equations, we have-

${20}^{2} + {90}^{2} = {70}^{2} + {DA}^{2}$

$400 + 8100 = 4900 + {DA}^{2}$

${DA}^{2} = 400 + 8100 - 4900 = 3600$

${DA} = \sqrt{3600}$

DA = 60cm

Hence, the value of DA is 60

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