Question

1. The height of a parallelogram is one-third of its base. If the area is 108 cm2, find the
base and height.​

Answer 1

Given:

• The Height of a parallelogram is one - third of its base.
• Area of parallelogram is 108 cm².

⠀⠀⠀

To find:

• Base and Height of parallelogram?

⠀⠀⠀

Solution:

⠀⠀⠀

☯ Let's consider base of parallelogram be x.

Therefore, Height of parallelogram will be x/3.

⠀⠀⠀

$\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(6,1)\qbezier(1,1)(1,1)(2,4)\qbezier(2,4)(1.6,4)(7,4)\qbezier(6,1)(6,1)(7,4)\qbezier(2,4)(2,4)(2,1)\put(0.5,0.5){\sf B}\put(6,0.5){\sf C}\put(1.8,4.3){\sf A}\put(7,4.3){\sf D}\put(1.8,0.5){\sf P}\put(3.3,0.5){\sf x cm}\put(2.2,2.2){ \sf \dfrac{x}{3} \:cm }\end{picture}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

Given that,

⠀⠀⠀

• Area of parallelogram is 108 cm².

⠀⠀

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Area_{\;(parallelogram)} = Base \times Height}}}}$

$:\implies\sf x \times \dfrac{x}{3} = 108$

$:\implies\sf \dfrac{x^2}{3} = 108$

$:\implies\sf x^2 = 108 \times 3$

$:\implies\sf x^2 = 324$

$:\implies\sf \sqrt{x^2} = \sqrt{324}$

$:\implies{\underline{\boxed{\frak{\purple{x = 18}}}}}\;\bigstar$

Therefore,

⠀⠀⠀

• Base of parallelogram, x = 18 cm

• Height of parallelogram, x/3 = 18/3 = 6 cm

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

• Parallelogram:- A parallelogram is a four-sided flat shape whose opposite sides are both equal and parallel.

• Area of parallelogram = Base × Height

• Perimeter of parallelogram = 2 × (sum of lengths of adjacent sides)

Answer 2

$\sf \: Given \: \ratio$

The Height of a parallelogram is one - third of its base.

Area of parallelogram is 108 cm².

⠀⠀⠀

$\sf \: To \: Find \: \ratio$

Base and Height of parallelogram

$\sf \: solution$

⠀⠀⠀

Let's assume base of parallelogram be $\sf x$

Therefore, Height of parallelogram will be $\sf \frac{x}{3}$

Given,area of ||ogram =108 cm²

$\boxed{\mathbb\red{\fcolorbox{red}{purple}{Area\:of\:parallelogram=Base×Height}}}$

$\sf \implies \: x ( \frac{x}{3} ) = 108$

$\sf \implies \: {x}^{2} = 324$

$\sf \implies \: x = \sqrt{324}$

$\sf \implies \: \underline{\boxed{\sf{x = 18 \: cm }}}$

$\sf \huge \bigstar\: answer \bigstar$

• $\therefore$Base of parallelogram=x=18 cm

• Height of parallelogram=x/3=18/3=6 cm