Question

A triangle and a parallelogram have the
same base and the same area. If the sides
of 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.​

Answer 1

Step-by-step explanation:

Perimeter of Triangle

2S=26+28+30=84

⇒S=42cm

Area

s(s−a)(s−b)(s−c)

(Heron's formula)

Area =

42(42−26)(42−28)(42−30)

=

42×16×14×12

Area=336cm

2

Area of parallelogram = Area of triangle

⇒ h×28=336

⇒h=12cm

Height of parallelogram =12cm

Answer 2

$\huge\mathrm{Answer}$

Given

• Area of parallelogram = area of triangle
• Base of triangle = base of parallelogram
• Sides of triangle = 26 cm, 28 cm, 30 cm
• Base of parallelogram = 28 cm

To find

Let the height of the parallelogram be :- h

Solution

s = (a+b+c)/2

➡ s = ( 28+26+30) / 2

➡ s = 84/2

➡ s = 42

b × h = √(s( s-a)(s-b)(s-c) ) { All the numbers are under the square root }

➡ 28 × h = √(42(42-28)(42-26)(42-30))

➡ 28 × h = √(42 × 2688)

➡ 28 × h = √112896

➡ h = 336 / 28

➡ h = 12 cm

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Answer ⭐

The height of the parallelogram is 12 cm