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

Answer:

Hi friends

Step-by-step explanation:

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.

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Answer 2

Answer:

12

Step-by-step explanation:

$area \: of \: parallelogram \: is \: traingle \: area \\ base \: \times height = area \: of \: triange \\ 28 \times h = area \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ \sqrt{42 \times 14 \times 12 \times 16} where \: 42is \: s \: s \: is \:( a + b + c) \div 2 \\ \sqrt{14 \times 3 \times 14 \times 4 \times 3 \times 4 \times 4} \\ 14 \times 4 \times 3 \times 2 = 336 \\ therefore = 28 \times height = 336 \\ h = \frac{336}{28}$