Question

In rectangle ABCD diagonal AC=4x+7 and BD=5x+4.Find value of x.​

Answer 1

Answer:

In rectangle ABCD the diagonals are equal so

AC =BD

4x+7 = 5x+ 4

7-4 = 5x-4x

3=x

I hope it is correct

Answer 2

Answer :-

• The value of x is 3.

To find :-

• The value of x.

Step-by-step explanation :-

• Here, it is given that the two diagonals of the rectangle ABCD are 4x + 7 and 5x + 4 respectively.

We know that :-

$\bigstar$ Diagonals of a rectangle are equal and bisect each other.

Therefore,

$\longmapsto \: \sf{4x + 7 = 5x + 4}$

$\longmapsto \: \sf{4x - 5x + 7 = 4}$

$\longmapsto \: \sf{4x - 5x = 4 - 7}$

$\longmapsto \: \sf{- x = 4 - 7}$

$\longmapsto \: \sf{- x = - 3}$

Cancelling the negative signs,

$\longmapsto \: \sf{x = 3}$

Hence :-

• The value of x is 3.

-----------------------------------------------------------

Verification :-

• To check our answer, let's put 3 in the place of x and see whether LHS = RHS.

LHS

$\longmapsto\sf{4x + 7}$

$\longmapsto \: \sf{4 \times 3 + 7}$

$\longmapsto \: \sf{12 + 7}$

$\longmapsto \: \sf{19}$

RHS

$\longmapsto \sf5x + 4$

$\longmapsto \sf 5 \times 3 + 4$

$\sf \longmapsto 15 + 4$

$\sf \longmapsto 19$

LHS = RHS.

Hence verified!

________________________________