Question

a triangle and a parrellogram have same base and same area. if the sides of triangle are 20cm, 25cm, and 35cm, and the base side 25cm for the triangle as well as the parrellogram, find the verticle height of the parrellogram
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Answer 1

$\huge{\text{\underline{Question:-}}}$

A triangle and a parrellogram have same base and same area. if the sides of triangle are 20cm, 25cm, and 35cm, and the base side 25cm for the triangle as well as the parrellogram. Find the verticle height of the parrellogram.

$\huge{\text{\underline{Solution:-}}}$

Let the Length of the sides of the triangle be,

• a = 26 cm
• b = 28 cm
• c = 30 cm

Let s be the semi perimeter of the triangle.

s = (a + b + c) / 2

s = (26 + 28 + 30) / 2= 84 / 2 = 42 cm

$\large{\boxed{\text{s = 42 cm}}}$

$\bigstar{\textbf{\underline{Using\:heron’s\:formula}}}$

Area of the triangle = √s (s-a) (s-b) (s-c)

= √42(42 – 26) (46 – 28) (46 – 30)

= √42 × 16 × 14 × 12

= √7 × 6 × 16 × 2 × 7 × 6 × 2

= √7 × 7 × 6 × 6 × 16 × 2 × 2

= 7 × 6 × 4 × 2 = 336cm²

$\large{\boxed{\text{= 336 cm}}}$

Let height of parallelogram be h and Base = 28 [Given]

Area of parallelogram = Area of triangle

[Area of parallelogram = base × height]

28 × h = 336

h = 336 / 28 cm

$\large{\boxed{\text{h = 12 cm}}}$

Hence the height of the parallelogram is 12 cm.

__________________________________________

Answer 2

Answer:

Step-by-step explanation:

Given :-

A triangle and a parallelogram have same base and same area. if the sides of triangle are 20 cm, 25 cm, and 35 cm, and the base side 25 cm for the triangle as well as the parallelogram.

To Find :-

Height of the parallelogram.

Formula to be used :-

Area of the triangle = √s (s-a) (s-b) (s-c)

Solution :-

Let the Length of the sides of the triangle are a = 26 cm, b = 28 cm and c = 30 cm.

s = (a + b + c)/2

s = (26 + 28 + 30)/2

s = 84/2= 42 cm

s = 42 cm

Using heron’s formula,

⇒ Area of Triangle =  √s (s-a) (s-b) (s-c)

⇒ Area of Triangle = √42(42 – 26) (46 – 28) (46 – 30)

⇒ Area of Triangle = √42 × 16 × 14 × 12

⇒ Area of Triangle = √7×6×16×2×7×6×2

⇒ Area of Triangle = √7×7×6×6×16×2×2

⇒ Area of Triangle = 7×6×4×2

⇒ Area of Triangle = 336 cm²

Now, we will find Height

Area of parallelogram = Area of triangle

⇒ 28 × h = 336

⇒ h = 336/28 cm

⇒ h = 12 cm

Hence, the height of the parallelogram is 12 cm.