Question

If the sides of A triangle and a parallelogram have the same base and the 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. Please don't spam.​

Answer 1

Answer:

If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, we have found that the height of the parallelogram is 12 cm.

Answer 2

The height of the parallelogram is12cm.

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.