Question

5. The length and breath
of a rectangle are
3x^2-2 and 2X+5respectively.
find its area-​

Answer 1

Answer:

Area of the rectangle = 6x³+15x²-4x-10

Step-by-step explanation:

Given :

Length = $\tt{{3x}^{2}-2}$

Breadth = $\tt{2x+5}$

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(2,3.5){\sf\large 3x^2-2 }\put(-1.8,1.4){\sf\large 2x+5}\put(-0.5,-0.4){\bf D}\put(-0.5,3.2){\bf A}\put(5.3,-0.4){\bf C}\put(5.3,3.2){\bf B}\end{picture}$

To find :

The area of the rectangle

Taken :

To find the area of the rectangle use this formula -:

$\boxed{\tt{A=L\:\times\:B}}$

Where,

A = Area of the rectangle

L = Length

B = Breadth

Solution :

$:\implies\tt{A=({3x}^{2}-2)\times(2x+5)}$

$:\implies\tt{A={3x}^{2}(2x+5)-2(2x+5)}$

Use cross multiplication

$:\implies\tt{A={6x}^{3}+{15x}^{2}-4x-10}$

So , the area of the rectangle is 6x³+15x²+4x+10 .

Extra :

Perimeter -:

$:\implies\tt{P=2({3x}^{2}-2+2x+5)}$

$:\implies\tt{P={6x}^{2}-4+4x+10}$

$:\implies\tt{P={6x}^{2}+4x+10-4}$

$:\implies\tt{P={6x}^{2}+4x+6}$

So , the perimeter of the rectangle is 6x²+4x+6 .

Answer 2

Answer:

Area = 6x³ + 15x² - 4x - 10

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\underline{\textsf{\textbf{ \red{ Given}}}}}}}}$

• $\bf\longrightarrow$Length of Rectangle = $\sf{3x^2-2}$

• $\bf\longrightarrow$Breadth of Rectangle= $\sf{2x+5}$

$\huge{\boxed{\boxed{\underline{\underline{\textsf{\textbf{ \red{ To\:Find}}}}}}}}$

• $\bf\longrightarrow$ Its Area

$\huge{\boxed{\boxed{\underline{\underline{\textsf{\textbf{ \red{Solution }}}}}}}}$

We know that Area of a Rectangle :-

• $\boxed{\sf Area = Length \times Breadth}$

• $\boxed{\sf Area =\sf{(3x^2-2)} \times (2x + 5)}$

• Explanation in 2nd Picture

• $\huge\bf\longrightarrow$ $\sf 6x^3+15x^2-4x-10$

Fig 1 = Picture of Rectangle