Question

A triangle and a parallelogram have the same base and the same area. If the sides
the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base
28 cm, find the height of the parallelogram.
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Answer 1

Answer:

Given A triangle and a parallelogram stands on same base and having same area ✓

And the dimensions of triangle are given

So, let us first find the area of the triangle which is as follows :-

But we can see the triangle is a scalan triangle so it's area can be find by using herons formula that is

$\boxed {\red{ \: area = \sqrt{s(s - a)(s - b)(s - c)}} }$

So for this we need to first find out the semiperimiter (S)

$= > s = \frac{28 + 30 + 26}{2} \\ = > = \frac{84}{2} \\ = > s = 42$

$\therefore{ \: area = \sqrt{42(42 - 28)(42 - 30)(42 - 26)} } \\ \\ = > area = \sqrt{42 \times 14 \times 12 \times 16} \\ \\ = > area = \sqrt{3 \times 7 \times 2 \times 7 \times 2 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ \\ = > area = \sqrt{3 ^{2} \times 7 ^{2} \times 2 ^{8} } \\ \\ = > area = 3 \times 7 \times 2 ^{4} \\ \\ = > area = 336 \: cm ^{2}$

And now given area of the triangle = area of the parallelogram

•°• Area of the parallelogram = 336 cm²

$= > base \times height = 336$

because area of parellelogram = base × height

$= > 28 \times height = 336 \\ \\ = > height = \frac{336}{28} \\ \\ = > \huge{\boxed{\red{\boxed{height = 12 \: cm}}}}$