Question

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

Answer 1

Given :

• diagonals of rectangle = (2x + 6)cm and (3x + 4)cm

To Find :

• find value of x and length of diagonal ?

Solution :

we know that,

★ diagonals of rectangle are equal to each other.

$: \implies 2x + 6 = 3x + 4 \\ \\ : \implies 3x - 2x = 6 - 4 \\ \\ : \implies \boxed{x = 2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, value of x is 2

then,

$\bold{diagonal = 2(2) + 6} \\ \\ : \implies 4 + 6 \\ \\ \: \: \: \: : \implies \boxed{10 \: cm} \\ \\ \bold{and} \\ \\ \: \: \: \: \: : \implies 3(2) + 4 \\ \\ : \implies 6 + 4 \: \: \\ \\ \: : \implies \boxed{10 \: cm}$

so, length of diagonal of rectangle is 10 cm

_______________________________

hence,

• value of x is 2
• length of diagonal of rectangle is 10 cm