Question

A triangle and a parallelogram have the same base and the saine area. If the sides of the triangle
are 26 cm, 28 cm and 30 en, and the parallelogram slands on the base 28 cm, find the height of
the parallelogram​

Answer 1

Answer:

Area of parallelogram = Area of triangle

Base × height = area of triangle

28 × height = area of triangle

Height = 1/28 × area of triangle

Finding area of triangle

Area of triangle =

$\sqrt{} s(s - a) \: (s - b) \: (s - c)$

Here, S is the semi - perimeter,

and a, b, c are the sides of triangle

Here a= 26, b= 28, and c= 30

$s = \frac{a + b + c}{2 \: } = \frac{26 + 28 + 30}{2} = \frac{84}{2 } = 42m$

Area of triangle =

$\sqrt{42(42 - 26)(42 - 28)(42 - 30)cm {}^{2} }$

$\sqrt{42(16)(14)(12)}$

$\sqrt{(14 \times 3) \times (16) \times (14) \times (12)}$

$\sqrt{(14 \times 14) \times (12 \times 3) \times (16)}$

$\sqrt{(14 \times 14) \times (12 \times 3) \times (16)}$

$\sqrt{(14 {}^{2} } ) \times (6 {}^{2} ) \times (4 {}^{2} )$

14 × 6 × 4 =

$336 \: cm {}^{2}$

Now, height = 1/28 × area of triangle

Height = 1/28×336

Height =12cm

Therefore, the height of the parallelogram = 12 cm