Question

the length and breadth of a triangle are in the ratio 5.2 and its perimeter is 98 cm find the area of the region bounded by the rectangle​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{Given:-}}$

$\sf\bullet Length\:and\: breadth\:of\: rectangle\:in\:ratio\\ \\ \sf:\implies 5:2\\ \\ \sf\:\:\bullet Perimeter=98cm$

Now The

$\boxed{\sf{Perimeter\:of\: rectangle=2(length+breadth)}}$

• Let the sides be x.

• Then 5x and 2x

$\sf:\implies 98=2(5x+2x)\\ \\ \sf:\implies \cancel{\dfrac{98}{2}}=7x\\ \\ \sf:\implies 49=7x\\ \\ \sf:\implies \cancel{\dfrac{49}{7}}=x\\ \\ \sf:\implies x=7cm$

• The value of x is 7 cm

• Now the sides

• 5×7= 35cm

• 2×7= 14cm

Now we have to find the Area of rectangle

$\boxed{\sf{Area\:of\: rectangle=length\times breadth}}$

$\sf\leadsto Sides =35cm\:\:and\:\:14cm\\ \\ \sf:\implies Area=35\times 14\\ \\ \sf:\implies Area=490cm{}^{2}$

$\boxed{\sf{Area\:of\:region=490cm{}^{2}}}$

Answer 2

Step-by-step explanation:

Given :

• The length and breadth of the rectangle are in the ratio : 5:2
• The perimeter of the rectangle = 98 cm

To Find :

• The area of the rectangle.

Let the length and breadth of the rectangle be 5x cm and 2x cm.

$\fbox {\pink {Perimeter = 2 (Length +breadth)}}$

$\implies Perimeter = 2 (Length +breadth) \\ \implies 98= 2 (5x + 2x) \\ \implies 98= 2 \times 7x \\ \implies 98 = 14x \\ \implies \frac{98}{14} = x \\ \implies 7 = x \\ \implies x = 7$

$\boxed {Length \:of \:the \:rectangle = (5\times 7)\:cm=35\:cm}$

$\boxed {Breadth \:of \:the \:rectangle = (2\times 7)\:cm=14\:cm}$

$\boxed {\purple {Area=Length\times Breadth}}$

$\implies Area=Length\times Breadth \\ \implies Area = 35 \: cm \times 14 \: cm \\ \implies Area = 490 \: cm^2$

$\boxed{\green {\therefore{The\: area\: of \:the\: rectangle = 490 \: cm^2}}}$