The area of a parallelogram is 98 cm². If one altitude is half the corresponding base, then<br />determine the base and the altitude of the parallelogram.<br />
Answers
Answer:
TheQuestion:
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:}}}
YourAnswer:
\sf{Given\:is\:that:}Givenisthat:
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 :-
\begin{gathered}\tt{h = \frac{b}{2}}\\\end{gathered}
h=
2
b
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}98=b×h
Put the value of h, we obtained from the above discussion:-
=》 \begin{gathered}\tt{98 = b \times \frac{b}{2}}\\\end{gathered}
98=b×
2
b
Take 2 on the L.H.S. and then solve it:-
=》 \tt{98\times 2 = b^{2}}98×2=b
2
Multiply 196 by 2 and then find the value of b :-
=》 \tt{196 = b^{2}}196=b
2
Do square root and then find the value of b :-
=》 \tt{b = \sqrt{196}}b=
196
The value of b is:-
=》 \tt{b = 14 cm}b=14cm
Thus, the base is = 14 cm
Height of the parallelogram = \begin{gathered}\tt{\frac{b}{2}}\\\end{gathered}
2
b
Height = \begin{gathered}\tt{\frac{14}{2}}\\\end{gathered}
2
14
Height of the parallelogram = \tt{7 cm}7cm
We found that :-
Base = 14 cm
Height = 7 cm
area = base into height
base = 2 height
98 = 2 into x into x
98 divided by 2 = x square
49 = x square
7 = x