Question

The area of a parallelogram is 98 cm². If one altitude is half the corresponding base, then
determine the base and the altitude of the parallelogram.
​

Answer 1

Let

• $\small \sf{The \: corresponding \: base \: be \: x.}$
• $\small \sf{Then \: Altitude \: will \: be \: \dfrac{x}{2} }$
• $\small \sf{Area \: of \: Parallelogram \: = 98 \: cm²}$

We know that

$\\\bf{Area \: of \: Parallelogram \: = altitude \times corresponding \: base}$

• Putting the value in Formula, we get

$\sf{~~~~~:~~\implies 98 = x \times \dfrac{x}{2} }$

$\sf{~~~~~:~~\implies {x}^{2} = 98 \times 2 }$

$\sf{ ~~~~~:~~\implies {x}^{2} = 196 }$

$\sf{~~~~~:~~\implies x = \sqrt{196} }$

$\sf{ ~~~~~:~~\implies x = 14 }$

Hance,

• $\small \sf{The \: corresponding \: base \: be \:\underline{\bf 14cm.}}$
• $\small \sf{Then \: Altitude \: will \: be \:\underline{\bf 7cm.} }$

Figure

• $\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$