Question

what is the answer to this problem with complete solution please.. for my homework thanks
The two consecutive sides of a parallelogram measures (10x-5) cm and (5x+10) cm, respectively. If the perimeter of the parallelogram measures 250 cm, then what is the measure of each side?

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

☯ Given :

First Side of parallelogram (A) = (10x - 5) cm

Second Side of parallelogram (B) = (5x + 10) cm

Perimeter of parallelogram = 250 cm

__________________________

☯ To Find :

We have to find the measure of each side of parallelogram.

__________________________

☯ Solution :

We know the formula to find the perimeter of parallelogram.

$\Large{\implies{\boxed{\boxed{\sf{Perimeter = 2(A + B)}}}}}$

________________[Put Values]

$\sf{→ 250 = 2\bigg((10x - 5) + (5x + 10)\bigg)} \\ \\ \sf{→ 250 = 2(10x - 5 + 5x + 10)} \\ \\ \sf{→ \frac{\cancel{250}}{\cancel{2}}= 15x + 5} \\ \\ \sf{→ 125 = 15x + 5} \\ \\ \sf{→ 15x = 125 - 5} \\ \\ \sf{→ 15x = 120} \\ \\ \sf{→x = \frac{\cancel{120}}{\cancel{15}}} \\ \\ \sf{→ x = 8} \\ \\ \Large{\implies{\boxed{\boxed{\sf{x = 8}}}}}$

$\therefore$ A = (10x - 5) = 10(8) - 5 = 80 - 5 = 75

B = 5x + 10 = 5(8) + 10 = 40 + 10 = 50

Answer 2

${ \huge \bf{ \mid{ \overline{ \underline{ \pink{QUESTION}}}} \mid}} \longrightarrow$

The two consecutive sides of a parallelogram measures (10x-5) cm and (5x+10) cm, respectively. If the perimeter of the parallelogram measures 250 cm, then what is the measure of each side?

__________________________

${ \huge{ \mathbb{ \overbrace{ \underbrace{ \purple{ANSWER}}}}}}$

$\huge{ \underline{ \green{given}}} = >$

• sides of parallelogram:-(10x-5)and(5x+10)cm.

• perimeter of parallelogram:-250cm.

$\huge{ \underline{ \green{solution}}} = >$

$\large \boxed{ \fbox{ \red{perimeter = 2(sum \: of \: both \: sides}}}$

$250 = 2(10x - 5) + (5x + 10) \\ = > 250 = 2(10x - 5 + 5x + 10) \\ = > \sf{ \cancel{ \dfrac{250}{2}}} = 15x + 5 \\ = > 125 = 15x + 5 \\ 15x = 120 \\ x = \sf{ \cancel{ \dfrac{120}{15}}}8 \\ = > \boxed{ \fbox{ x = 8}}$

$\\ = > first \: number = 10x - 5 \\ = > 10 \times 8 - 5 \\ = > 75 \\ \large \boxed{ \fbox{ \purple{first \: number = 75}}} \\ second \: number = 5x + 10 = 5 \times 8 + 10 \\ = 40 + 10 \\ = > 50 \\ \large \boxed{ \fbox{ \purple{second \: number = 50}}}$