Question

The height and base of a parallelogram are in the ratio 5:4. If the area of the parallelogram is 1620 sq.m, then find the base and altitude.
(2 Points)​

Answer 1

Answer:

Hope it will help you...

Answer 2

The base and the altitude of the parallelogram are 36 m and 45 m respectively.

Step-by-step explanation:

${\underline{\underline{\bf{Given:}}}}$

• The ratio of height and the base of the parallelogram = 5 : 4
• Area of the parallelogram = 1620 m²

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The length of base and altitude (height).

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{(||-gram)}=bh\:sq.units}}}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:b=base}$

$\:\:\:\:\:\:\:\:\sf{\bullet\:h=height}$

${\underline{\underline{\bf{Solution:}}}}$

Let the measures of base and height be $\bf{5x}$ and $\bf{4x}$, respectively.

As the measure of area of the ||-gram is given, we can find the value of $\bf{x}$ by, substituting the measures in the formula:

$\leadsto{\sf{\purple{Area=bh\:sq.units}}}$

$\:\:\:\:\:\:\::\implies{\sf{1620=5x\times 4x}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\::\implies{\sf{1620=20\times x^2}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{162\cancel{0}}{2\cancel{0}}=x^2}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{81=x^2}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\sqrt{81}=x}}$

$\:$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies\underline{\bf{9=x}}$

${\boxed{\textsf{\orange{The value of x is \underline{\bf{ 9 }}}}}}$

Hence,

• Altitude $\bf{(5x)\sf{=5\times 9={\underline{\underline{\red{45\:m}}}}}}$
• Base $\bf{(4x)\sf{=4\times 9={\underline{\underline{\red{36\:m}}}}}}$

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