Question

In a parallelogram ABCD, AB =(3x+7)cm and CD=(12-2x)cm.Find x ,hence the length of AB is equal to.

8cm.

14cm.

4cm.

10cm.​

Answer 1

Answer:

1 and 10 cm

Step-by-step explanation:

It is stated in the question that: In a parallelogram ABCD, length of AB is ( 3x + 7 ) cm and the. length of CD is ( 12 - 2x ) cm.

We've been asked to calculate the value of x and length of AB.

We know, that opposite sides of parallelogram are equal. So,

$\twoheadrightarrow\quad\sf{{Length}_{(AB)}={Length}_{(CD)}}$

Equating the values.

$\twoheadrightarrow\quad\sf{3x+7=12-2x}$

Transposing -2x from RHS to LHS. It's sign will get change.

$\twoheadrightarrow\quad\sf{3x+7+2x=12}$

Transposing +7 from LHS to RHS. It's sign will get change.

$\twoheadrightarrow\quad\sf{3x+2x=12-7}$

Performing subtraction in RHS and addition in LHS.

$\twoheadrightarrow\quad\sf{5x=5}$

Transposing 5 from LHS to RHS. It's arithmetic operator will get change.

$\twoheadrightarrow\quad\sf{x=\dfrac{5}{5}}$

Performing division in order to calculate the value of x.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{x=1}}}}$

Here, we've calculated the value of x that is 1. So, according to the question, length of AB is ( 3x + 7 ) cm. So,

$\twoheadrightarrow\quad\sf{AB=3x+7}$

Equating value of x in order to perform multiplication.

$\twoheadrightarrow\quad\sf{AB=3(1)+7}$

Performing multiplication.

$\twoheadrightarrow\quad\sf{AB=3+7}$

Performing addition in order to calculate the length of AB.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{AB=10\; cm}}}}$

❝ Therefore, value of x is 1 and length of AB is 10 cm. ❞