Question

The perimeter of a rectangle is 230 cm. If the length of the rectangle is 70 cm, find its
breadth and area?

Answer 1

Given that, Perimeter of a rectangle is 230 cm. & the length of rectangle is 70 cm.

We've to find out the breadth of the rectangle.

❍ So Let say, that the breadth of the rectangle be x.

As we know that,

$\bigstar\;{\underline{\boxed{\frak{Perimeter_{\:(rectangle)} = 2\Big(length + breadth\Big)}}}}$ ⠀⠀⠀

⠀⠀⠀

$\frak{we\;have}\begin{cases}\sf{\:\; \: Breadth = \bf{x\;cm}}\\\sf{ \: \: \: Length = \bf{70 \;cm}}\\\sf{ \: \: \: Perimeter = \bf{230\;cm}}\end{cases}$ ⠀⠀⠀⠀⠀⠀

⠀⠀⠀

⠀⠀⠀$\underline{\bf{\dag} \:\mathfrak{Substituting\;given\;values\;in\;formula\;:}}$⠀

⠀⠀⠀

$\dashrightarrow\sf 230 = 2\Big\{70 + x\Big\} \\\\\\\dashrightarrow\sf 230 = 140 + 2x\\\\\\\dashrightarrow\sf 2x = 230 - 140\\\\\\\dashrightarrow\sf 2x = 90\\\\\\\dashrightarrow\sf x = \cancel\dfrac{90}{2} \\\\\\\dashrightarrow\underline{\boxed{\pmb{\frak{\pink{x = 45}}}}}\;\bigstar$

⠀⠀⠀

Therefore, the Length and Breadth of the rectangle are 70 cm & 45 cm respectively.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

¤ Now, we know both dimensions of the rectangle. We can find out the area of rectangle by using the formula given below —

⠀⠀⠀

$\twoheadrightarrow\sf Area = \Big\{Length \times Breadth\Big\} \\\\\\\twoheadrightarrow\sf Area = 45 \times 70 \\\\\\\twoheadrightarrow\underline{\boxed{\pmb{\frak{\purple{ Area = 3150\;cm^2}}}}}\;\bigstar$

⠀⠀

$\therefore{\underline{\sf{Hence, \; area\;of\;the\;given\; rectangle\;is\;\bf{3150\;cm^2}.}}}$

Answer 2

Answer:

hope it help you.

good evening.