Question

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Answer 1

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

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Answer 2

Answer:

The given sides of the traingle are 13cm, 14cm and 15cm. Let a=13cm, b=14cm and c=15cm.

So, semi-perimeter of the triangle is:

s= (a+b+c)/2 = (13 + 14 + 15)/2 = 21 cm

We know,

The area of a triangle is:

A = [s(s-a)(s-b)(s-c)]^1/2

=[21(21-13)(21-14)(21-15)]^1/2

=[21×8×7×6]^1/2

=[7056]^1/2

=84 cm^2

Now,

The area of the triangle and parallelogram is same and both have same bas i.e. 14 cm.

So,

The area of parallelogram is also:

A=84 cm^2

or, b×h=84 [As area of parallelogram = b×h]

or, 14×h=84

or,h = 84/14

Hence, h = 6cm

Thus, the required height of the parallelogram is 6cm.

Step-by-step explanation:

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