Question

A quadrilateral can be constructed uniquely if the lengths of its and diagonal is known. sides

a. 1,4

b. 2, 3

c. 4, 1

d. 4, 3​

Answer 1

Given,

A quadrilateral can be constructed uniquely if the lengths of its and diagonal is known. sides

a. 1,4

b. 2, 3

c. 4, 1

d. 4, 3​

Solution,

Know that the length of each diagonal is equal to the square root of the sum of the squares of two consecutive sides of the quadrilateral.

Therefore,

$\[\begin{array}{l} \Rightarrow \sqrt {{4^2} + {3^2}} \\ \Rightarrow \sqrt {16 + 9} \\ \Rightarrow \sqrt {25} \\ \Rightarrow 5\end{array}\]$

Hence, the correct option is (d) i.e. $\[\left( {4,3} \right).\]$