Question

XOYZ is a rectangle with vertices X(-3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each diagonal is ______.

पर्याय

• 5 units

• `sqrt5` units

• x² + y² units

• 4 units

Answer 1

XOYZ is a rectangle with vertices X(-3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each diagonal is 5 units.

Explanation:

Given

We know that, Length of Diagonals are equal in Rectangle 

ZO = YX

⇒ `sqrt((x - 0)^2 + (y - 0)^2) = sqrt((0 + 3)^2 + (4 - 0)^2)`

⇒ `sqrt(x^2 + y^2) = sqrt25`

⇒ x² + y² = 5 Both Diagonal are 5 units 

OR

(ZO)² = (ZX)² + (XO)²

(ZO)² = 4² + 3²

(ZO)² = 25

ZO = 5

Again (YX)² = (YO)² + (XO)² = 4² + 3²

(YX)² = 25 

YX = 5