Question

The height of a parallelogram is one-third of its base. if the area is 108 sq. cm, find the base and height 9p OK​

Answer 1

Given -

• The height of a parallelogram is one-third of its base.

• Area of parallelogram = 108cm²

To find -

• Height and base.

Solution -

Here, we are given with the area of the parallelogram, and it's height is 1/3 of it's base, and we need to find the height and base. For that we will use the formula of area of parallelogram, and will solve the further calculations.

So -

Let the height be termed as x

Therefore, base will be 1/3x

Area is 108cm²

Now -

Area of parallelogram = B × H

where -

B = base

H = Height

On substituting the values -

Area = B × H

$\longrightarrow$ $\sf\dfrac{1}{3}$x × x = 180cm²

$\longrightarrow$ $\sf\dfrac{1}{3}$ x² = 108cm²

$\longrightarrow$ x² = 108 × 3

$\longrightarrow$ x² = 324

$\longrightarrow$ x = $\sf\sqrt{324}$

$\longrightarrow$ x = 18 cm

Similarly -

$\longrightarrow$ Height = $\sf\dfrac{1}{3}$ × 18

$\longrightarrow$ Height = 6 cm

Verification -

Area = B × H

108cm² = 18 cm × 6 cm

108cm² = 108cm²

$\therefore$ Height and base of the parallelogram is 18 cm and 6 cm

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Answer 2

Step-by-step explanation:

$\setlength {\unitlength}{1cm}\begin {picture}(0,0)\thicklines\qbezier (0,0)(0,0)(5,0)\qbezier (0,0)(0,0)(1,3)\qbezier (1,3)(1,3)(6,3)\qbezier (5,0)(5,0)(6,3)\qbezier(1,3)(1,3)(1,0)\put (1.2,1.5){\sf 6\:cm}\put (2,-0.5){\sf 18\:cm}\\end {picture}$

Given:-

• Area of a parallelogram =108 sq.cm
• The height of the parallelogram is one third of its base.

To find:-

• Height and base of the parallelogram

Solution:-

Let

• Base= x cm
• Height =1/3 cm

As we know that in a parallelogram

$\boxed {\bf Area=Base\times Height}$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow \dfrac {1}{3}x\times x=108$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow \dfrac {1}{3}x^2=108$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x^2=108\times 3$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x^2=324$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x=\sqrt {324}$

$\\\qquad\quad\displaystyle\bf {:}\longrightarrow x=18$

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Breadth = 18 cm

Height =1/3×18=6 cm

$\therefore\bf Height\:is\:6cm.$

$\therefore\bf Base\:is\:18\:cm.$