Question

the side of rectangle are in the ratio 4: 5 and its perimeter is 90 cm ; find the demensions of the rectangle and its area

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Answer 1

$\huge\underline\mathfrak{Answer-}$

$\large{\boxed{\tt{\pink{Length\:of\:rectangle=20\:cm}}}}$

$\large{\boxed{\tt{\blue{Breadth\:of\:rectangle=25\:cm}}}}$

$\large{\boxed{\tt{\green{Area\:of\:rectangle=500\:cm^2}}}}$

$\huge\underline\mathfrak{Explanation-}$

Given :

• Ratio of sides of rectangle is 4:5
• Perimeter of rectangle is 90 cm.

To find :

• Length of rectangle
• breadth of rectangle
• area of rectangle

Figure :

$\setlength{\unitlength}{2cm}\begin{picture}(16,4)\thicklines\put(8,3){\circle*{0.1}}\put(7.8,3){\large{D}}\put(7.2,2){\mathsf{\large{?cm}}}\put(8,1){\circle*{0.1}}\put(7.8,1){\large{A}}\put(9.3,0.8){\mathsf{\large{?cm}}}\put(11.1,1){\large{B}}\put(8,1){\line(1,0){3}}\put(11,1,){\circle*{0.1}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11,3){\circle*{0.1}}\put(11.1,3){\large{C}}\end{picture}$

Formula used :

• Perimeter of rectangle = 2(L+B)
• area of rectangle = L × B

Solution :

The ratio of sides of rectangle is 4:5.

Let length of rectangle be 4x and breadth be 5x.

Now, by using perimeter of rectangle,

Perimeter of rectangle = 2(L+B)

$\implies$ 90 = 2(4x+5x)

$\implies$ 9x = $\cancel{\dfrac{90}{2}}$

$\implies$ 9x = 45

$\implies$ x = $\cancel{\dfrac{45}{9}}$

$\implies$ x = 5

$\rule{200}3$

★ Length of rectangle = 4x

$\implies$ Length of rectangle = 4 × 5

$\large{\boxed{\tt{\pink{Length\:of\:rectangle=20\:cm}}}}$

★ Breadth of rectangle = 5x

$\implies$ Breadth of rectangle = 5 × 5

$\large{\boxed{\tt{\blue{Breadth\:of\:rectangle=25\:cm}}}}$

$\rule{200}3$

★ Area of rectangle = L × B

$\implies$ Area of rectangle = 20 × 25

$\large{\boxed{\tt{\green{Area\:of\:rectangle=500\:cm^2}}}}$

Answer 2

Answer:

Length of Rectangle = 20cm

Breadth of Rectangle = 25cm

Area of Rectangle = 500cm²

Step-by-step explanation:

We Have :-

Ratio of sides of rectangles = 4:5

Perimeter of Rectangle = 90 cm

To Find :-

Sides of Rectangle

Area of Rectangle

Formula Used :-

Perimeter of Rectangle = 2 ( Length + Breadth )

Area of Rectangle = Length * Breadth

Solution :-

Let the Length of Rectangle be 4x

Let the Breadth of Rectangle be 5x

$Perimeter\ of\ Rectangle = 2 ( 4x + 5x )\\\\90=2(9x)\\\\9x=45\\\\x= 5$

$Length\ of\ Rectangle = 4x\\\\= 4*5\\\\= 20 cm\\\\Breadth\ of\ Rectangle = 5x\\\\=5*5\\\\= 25 cm$

$Area\ of\ Rectangle = Length*Breadth\\\\= 20 * 25\\\\= 500cm^{2}$