Math, asked by Divjyotsingh2305, 1 year ago

the area of a parallelogram is 98 cm square. if one altitude is half the corresponding base, determine the base and the altitude of the parallelogram

Answers

Answered by Anonymous
65
altitude=14m
base=7 m
Attachments:
Answered by mathsdude85
13

\underline{\mathfrak{\huge{The\:Question:}}}

The area of parallelogram is 98 cm square. If one of the altitude is half of the corresponding base, determine the base and altitude of the parallelogram.

\underline{\mathfrak{\huge{Your\:Answer:}}}

\sf{Given\:is\:that:}

Area of the parallelogram = 98 sq. cm

If we let the base to be equal to b, and the corresponding height to be equal to h, it's given that :-

\tt{h = \frac{b}{2}}\\

Now, we know that, the area of any parallelogram is :-

Area of a parallelogram = Base × Height = b × h

Put the values in the formula, and then, simply solve it, you will get your answer :-

=》 \tt{98 = b \times h}

Put the value of h, we obtained from the above discussion:-

=》 \tt{98 = b \times \frac{b}{2}}\\

Take 2 on the L.H.S. and then solve it:-

=》 \tt{98\times 2 = b^{2}}

Multiply 196 by 2 and then find the value of b :-

=》 \tt{196 = b^{2}}

Do square root and then find the value of b :-

=》 \tt{b = \sqrt{196}}

The value of b is:-

=》 \tt{b = 14 cm}

Thus, the base is = 14 cm

Height of the parallelogram = \tt{\frac{b}{2}}\\

Height = \tt{\frac{14}{2}}\\

Height of the parallelogram = \tt{7 cm}

We found that :-

Base = 14 cm

Height = 7 cm

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