Question

The area of a parallelogram is 392m2. If its altitude is twice the corresponding base, then the  altitude is ............................ m.            ​

Answer 1

AnswEr:-

$\sf \Box$ Altitude of parallelogram = 28 m

$\rule{200}{1}$

Given:-

• Area of parallelogram = 392 m²
• Altitude = 2 × corresponding base.

To find :-

• Altitude of parallelogram = ?

Solution :-

Let the base of parallelogram be B m.

So,altitude of parallelogram = 2B m

We know,

$\bf{\dag}\: \large{\boxed{\rm{\blue{Area \: of \: parallelogram = Base \times Altitude }}}}$

• Putting values:-

$\dashrightarrow\sf B \times 2B = 392 \\\\\dashrightarrow\sf 2B^2 = 392 \\\\\dashrightarrow\sf B^2 = 392/2 \\\\\dashrightarrow\sf B^2 = 196 \\\\\dashrightarrow\sf B = \sqrt{196} \\\\\dashrightarrow\large{\underline{\boxed{\rm{\red{B = 14 \: m }}}}}\: \star$

$\rule{100}{2}$

⋆ DIMENSIONS:-

↠ Base = B = 14 m

↠ Altitude = 2B = 2 × 14 = 28 m

$\therefore\underline{\textsf{Altitude\: of \: parallelogram = {\textbf{28 \: m }}}}$

Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{A}}\put(7.7,0.9){\large{B}}\put(9.5,0.7){\sf{\large{x m}}}\put(11.1,0.9){\large{C}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(9.1,2){\sf{\large{2x m}}}\put(9,1){\line(0,1){2}}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{D}}\end{picture}$

$\rule{160}{1}$

Let the Base of Parallelogram be x m, and Corresponding Altitude be 2x m.

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\:Area_{\parallel gram}=Base\times Altitude\\\\\\\dashrightarrow\tt\:\:392\:{m}^{2} =x \:m \times 2x\:m\\\\\\\dashrightarrow\tt\:\:392 \:{m}^{2} = 2x^{2}\:{m}^{2}\\\\\\\dashrightarrow\tt\:\: \dfrac{392 \: {m}^{2}}{2\:{m}^{2} } = {x}^{2}\\\\\\\dashrightarrow\tt\:\:196 = {x}^{2}\\\\\\\dashrightarrow\tt\:\: \sqrt{196} = x\\\\\\\dashrightarrow\tt\:\: \sqrt{(14 \times 14)} = x\\\\\\\dashrightarrow\tt\:\:x =14$

$\rule{200}{2}$

$\underline{\bigstar\:\:\textsf{Altitude of Parallelogram :}}$

$:\implies\tt Altitude=2x\:m\\\\\\:\implies\tt Altitude=2\times14\:m\\\\\\:\implies\underline{\boxed{\textsf{\textbf{Altitude = 28 m}}}}$