Question

A triangle and a parallelogram have a smae 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​

Answer 1

Solution:

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

s = 42 cm

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= 336 cm²

Let height of parallelogram be h.& Base= 28 (given)

Area of parallelogram = Area of triangle (given)

[Area of parallelogram =base× height]

28× h = 336

h = 336/28 cm

h = 12 cm

Hence,

The height of the parallelogram is 12 cm.

Answer 2

Given :

a = 26 cm

b = 28 cm

c = 30 cm

.

.

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Let the height of the parallelogram be h cm.

Then, area of the parallelogram

= Base × Height = 28 × h ${cm}^{2}[\tex]</p><p></p><p></p><p>According to the Question :</p><p></p><p>[tex]\implies \: 28h \: = 336 \\ \implies \: h \: = \frac{336}{28} \\ \therefore \: h = 12 \: cm$