Question

quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x if JF is equal to 8x + 4 and EG is equal to 24x-8​

Answer 1

Answer

The value of x is 2

Explanation

Given, a rectangle EFGH in which the intersecting point of diagonals is marked as J.

Since it's a rectangle, the diagonals are equal and bisected by each other.

→ EG = FH

Also, JF = JH (since they are bisected by each other)

Here, we can see

JF + JH = FH

→ JF + JF = EG

→ 2JF = EG

→ JF = EG/2

Now put the values of JF and EG

→ 8x + 4 = (24x - 8)/2

→ 8x + 4 = 12x - 4

→ 4 + 4 = 12x - 8x

→ 8 = 4x

→ x = 2

Answer 2

Answer:

${\boxed{\bold{Answer: \: x = \: 2}}}$

Step-by-step explanation:

Given,

• $\bold\green{JF = 8x + 4}$
• $\bold\red{EG = 24x - 8}$
• $\bold\purple{x =?}$

As EFGH is a rectangle,so the diagonals must be equal.

$\therefore\sf EG = FH$

Again,

$\sf FH = JF + JH \\\rightarrow\sf JF + JF = FH \\\rightarrow\sf 2JF = FH$

In diagonal FH,

$\rightarrow\sf JF + JH = FH \\\\\rightarrow\sf 2JF = EG \\\\\rightarrow\sf 2 \times (8x + 4) = 24x - 8 \\\\\rightarrow\sf 16x + 8 = 24x - 8 \\\\\rightarrow\sf 16x - 24x = - 8 - 8 \\\\\rightarrow\sf - 8x = - 16 \\\\\rightarrow\sf x =\frac{-16}{-8}$

$\rightarrow{\boxed{\bold{x = 2}}}$

$\therefore\bold{\underline{Value\:of\:x = 2}}$