Question

If ABCD is a rectangle such that AC = 5x + 6 and BD = 26, then x =​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

GiveN:

• ABCD is a rectangle.
• AC = 5x + 6 cm
• BD = 26 cm

To FinD:

• Value of x?

Solution:

In ABCD rectangle, AC and BD are the diagonals.

A rectangle is a quadrilateral whose diagonals are equal and bisect each other is a rectangle. Then, AC = BD

➛ AC = BD (In measure)

➛ 5x + 6 cm = 26 cm

➛ 5x = 20 cm

➛ x = 4 cm.

Hence,

The value of x is:

$\large{ \boxed{ \sf{ \pink{4 \: cm}}}}$

Explore more!!

The known quadrilaterals with certain characteristics are as follows:

• Square - 4 sides equal and the diagonals are equal.

• Rectangle - Opposite sides equal and Diagonals are equal.

• Rhombus - All sides are equal but not the diagonals.

• Parallelogram - Opposite sides are equal but not diagonals.

Answer 2

Given :

• ABCD is a rectangle such that AC = 5x + 6 and BD = 26

To Find :

• Value of x

Solution :

• It is given ABCD is a rectangle and we know that diagonals of rectangle are equal i.e. AC is equal to BD

• Now , according to the question :

$\:\:\: \implies \: \sf AC\:=\:BD$

$\:\:\: \implies \: \sf 5x\:+\:6\:=\:26$

$\:\:\: \implies \: \sf 5x\:=\:26\:-\:6$

$\:\:\: \implies \: \sf 5x\:=\:20$

$\:\:\: \implies \: \sf x\:=\: \cancel \dfrac{20}{5}$

$\:\:\: \implies \: \sf x\:=\: 4$

$\bigstar\: {\sf{\underline{\pink{Value\:of\:x\:is\:4}}}}$

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VeRiFiCaTiOn :

• Let us find measure of diagonal AC :

• Value of diagonal AC is 5x + 6

→ 5(4) + 6

→ 20 + 6

→ 26 cm , which is equal to diagonal BD , hence verified

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