Question

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

Answer 1

altitude=14m
base=7 m

Answer 2

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

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