Question

The length of a rectangle is 5 m greater than its width. If the perimeter of the recta 50 m. find its length​

Answer 1

$\\ \qquad{\rule{200pt}{3pt}}$

❒ Information given with us ,

➪ The length of a rectangle is 5 m greater than its width.

➪ The perimeter of the rectangle is 50 m.

❒ What we have to find ?

➪ The required measure of length of rectangle

❒ Solution ❒

$\clubsuit$ Assume that ,

➪ Let the breadth of rectangle be x m

According to the condition given in question ,

➪The length of a rectangle is 5 m greater than its width.

➪ So the length is

$\dashrightarrow \sf \: (x + 5) \: m$

❒ Formula used ❒

$\clubsuit$ Perimeter of rectangle ,

$\qquad \pink{\: \:\bigstar \: {\underline{\overline{\boxed{\sf{ 2 \times (l + b) }}}}} \: \bigstar}$

$\clubsuit$ Where,

• ➪ l = Length of rectangle
• ➪ b = breadth of rectangle

❒ Now ❒

➪ Substituting the given values in above formula we get ,

$\dashrightarrow \sf \: 2 \times (x + x+ 5)$

$\dashrightarrow \bf\: 2 (2x + 5)$

❒ Given that ❒

$\clubsuit$ Perimeter of the rectangle is 50 m.

❒ So ❒

$\rm\implies \therefore \: 2 \times (2 \: x + 5) = 50$

$\rm\implies \: 4 \: x + 10 = 50$

$\rm\implies \: 4 \: x = 50 - 10$

$\rm\implies \: 4 \: x = 40$

$\rm\implies \:x = \dfrac{40}{4}$

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{ x = 10 }}}}} \: \bigstar}$

❒ Therefore ❒

➪ The required measure of length of rectangle is

$\clubsuit$ By substituting the value x = 10 in ( x + 5 ) we get ,

$: : \implies\sf\: \bigg((10) + 5 \bigg)$

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\sf{15 \: m }}}}} \: \bigstar}$

❒ Final answer ❒

${\large : : \implies\qquad {\: \bigstar \: {\underline{\overline{\boxed{\bf{Length = 15 \: m \: }}}}}\: \bigstar}}$

❒ Verification ❒

$: : \implies\sf\:50 = 2 \times (15 + 10)$

$: : \implies\sf\:50 = 2 \times (25)$

$: : \implies\sf\:50 = 50$

$: : \implies\bf\:L.H.S = R.H.S$

Answer 2

We have,

Breadth=x

Length=x+5

Perimeter=2(x+x+5)

∴50=2(2x+5)

=>$\frac{50}{2}$=2x+5

=>25=2x+5

=>2x=25−5

=>2x=20

=>x=$\frac{20}{2}$

=>x=10

∴ Breadth=10

Length=x+5

=10+5

=15

Hence, this is answer.

Hope it helps :)

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