Question

ABCD is a rectangle whose diagonals are (2x+6)cm and (3x+4)cm. find the value of x and the length of the diagonals
​

Answer 1

(3+4-6). =453988059597५+"+'५+;+

Answer 2

Answer:

The value of x is 2 cm and the length of the diagonals are 10 cm each .

Step-by-step explanation:

If we consider a rectangle ABCD  taking the two of it's diagonals AC and BD.

If we consider two of the triangles ABC and BCD.

Then we find that ,

AB = CD , BC is a common side and ∠ABC = ∠BCD = 90°

Hence , The triangles ABC and BCD are congruent.

so, AC = BD ( they are the corresponding sides of the two triangles )

∴ The diagonals of a rectangle are equal in length.

Hence ,  2x +6 = 3x + 4

⇒ 3x -2x = 6 - 4

⇒ x = 2 cm

∴ the length of the diagonals = 2×2 + 6 = 4 + 6 = 10 cm