Question

13) If AOBC is a rectangle whose three vertices are A(0,3), (0,0) and B(5,0).

Then sum of the squares of its both diagonals is units,
(a) 2root34
(b) 68
(c) 34
(d) 2root68​

Answer 1

(b) 68

Explanation:

Distance between two points:

Suppose that we have two points,
`(x_1,y_1)` and
`(x_2,y_2)`. The distance between them is given by:

`D = √((x_2-x_1)^2+(y_2-y_1)^2)`

Diagonal:

Diagonals are a line between opposite points in a square.

In this question, it is between A(0,3) and B(5,0), and between (0,0) and (5,3). Both these diagonals have the same measure, and are the distance between these points. So

`D = √((5-0)^2+(3-0)^2) = √(5^2 + 3^2) = √(34)`

Then sum of the squares of its both diagonals is units

Both diagonals measure
`√(34)`. Sum of squares is:

`(√(34))^2 + (√(34))^2 = 34 + 34 = 68`

The correct answer is given by option b.