Question

A triangle and a parallelogram have the same base and same area. If the sides of the triangle are 15 cm, 14 cm and 13 cm and the parallelogram stands on the base 15 cm, find the height of the parallelogram

Answer 1

Answer:

$\boxed{\red{\bf Height\:of\:parallelogram=5.6\:cm}}$

Step-by-step explanation:

Given that -

Area of parallelogram = Area of triangle

⇒ Base × Height = Area of triangle

⇒ 15cm × Height = Area of triangle

⇒ Height = $\dfrac{1}{15} *\text{Area\:of\:triangle}$

Let us find the area of triangle.

Area of triangle = $\sf \sqrt{s(s-a)(s-b)(s-c)}$

Here, s represents semi-perimeter, and a, b, c are the sides of the triangle.

• a = 15 cm
• b = 14 cm
• c = 13 cm

$\implies \text{s}=\dfrac{\text{a+b+c}}{2}$

$\implies \text{s}=\dfrac{15+14+13}{2}$

$\implies \text{s}=\dfrac{42}{2}$

$\implies \text{s}=21$

Area of triangle = $\sf \sqrt{s(s-a)(s-b)(s-c)}$

⇒Area= $\sf \sqrt{21(21-15)(21-14)(21-13)}$

⇒ Area = $\sf \sqrt{21*6*7*8}$

⇒ Area = $\sf \sqrt{7056}$

⇒ Area = 84 cm²

Now, Height = $\dfrac{1}{15} *\text{Area\:of\:triangle}$

⇒ Height = $\dfrac{1}{15}*84$

⇒ Height = 5.6 cm

Therefore, height of the parallelogram is 5.6 cm.

Answer 2

Hyy Dude

Heron's Formula

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 15 cm, 14 cm and 13 cm and the parallelogram stands on the base 15 cm, find the height of the parallelogram. Hence, the height of the parallelogram is 5.6 cm.

May this helps you

Plz marked in brainlest answer