Question

A Triangle and a parallelogram stand on the same base of 50cm Have the same area if the other side of the triangle are 30and 40 find the corresponding hight of the parlogram

Answer 1

Given:

A triangle and a parallelogram lie on the same base of length 50cm.

Both the triangle and the parallelogram have the same area.

The other two sides of the triangle are of 30 cm and 40 cm.

To find:

Find the height of the parallelogram.

Solution:

First, let's find the area of the triangle ABC using Heron's formula.

a = 50cm, b = 30cm, c = 40cm.

Semi-perimeter:

$\sf \Longrightarrow s = \dfrac{a + b + c}{2}$

$\sf \Longrightarrow s = \dfrac{50 + 30 + 40}{2}$

$\sf \Longrightarrow s = \dfrac{120}{2}$

$\sf \Longrightarrow s = 60 cm$

Now, using Heron's formula we get:

$\sf \Longrightarrow \triangle ABC = \sqrt{s(s-a)(s-b)(s-c)}$

$\sf \Longrightarrow \triangle ABC = \sqrt{60(60-50)(60-30)(60-40)}$

$\sf \Longrightarrow \triangle ABC = \sqrt{60(10)(30)(20)}$

$\sf \Longrightarrow \triangle ABC = \sqrt{(2 \times 2 \times 5 \times 3)(2 \times 5)(2 \times 3 \times 5)(2 \times 2 \times 5)}$

$\sf \Longrightarrow \triangle ABC = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 \times 5 \times 5}$

$\sf \Longrightarrow \triangle ABC = \sqrt{2^2 \times 2^2 \times 2^2 \times 3^2 \times 5^2 \times 5^2}$

$\sf \Longrightarrow \triangle ABC = 2 \times 2 \times 2 \times 3 \times 5 \times 5$

$\sf \Longrightarrow \triangle ABC = 600 cm^2$

ATQ, Area of the triangle is equal to the area of the parallelogram:

⇒ Area of Δgle = Area of a Parallelogram

⇒ 600 = b × h

⇒ 600 = 50 × h

⇒ 600/50 = h

⇒ h = 600/50

⇒ h = 12 cm

∴ The corresponding height of the parallelogram is 12cm.

Answer 2

Please see the following attachment.