Question

A triangle and parallelogram have the same base and the same area if the sides of the triangle are 26 cm and 28 cm and 37 cm and the Parallelogram stands on the base 28 cm ..find the height of the parallelogram..​

Answer 1

Question :

A triangle and parallelogram have the same base and the same area if the sides of the triangle are 26 cm and 28 cm and 37 cm and the Parallelogram stands on the base 28 cm ..find the height of the parallelogram..

Answer :

First we will find semi perimeter =

$\frac{26 + 30 + 28}{2} \\ \\ 42 \: cm$

Now,

$area = \sqrt{s(s - ab)(s - be)(s - ae)} \\ \\ area = \sqrt{42 \times 16 \times 14 \times 12} \\ \\ = \sqrt{6 \times 7 \times 4 \times 4 \times 7 \times 2 \times 2 \times 6} \\ \\ = 6 \times 7 \times 4 \times 2 \\ \\ = 336 \: cm {}^{2}$

Area of Parallegram = base × height

28 × h = 336

$h \: = \frac{366}{28} \\ \\ 12 \: cm$

Answer 2

Answer:

• Height of parallelogram is 12.98 cm.

Step-by-step explanation:

Given :

• Triangle and parallelogram are on same base.
• Both have same area's.
• Sides of triangle are 26 cm, 28 cm and 37 cm.
• Parallelogram stands on the base 28 cm.

To find :

• Height of parallelogram.

Solution :

Formula to be used :

• Heron's formula :

Area of triangle = √s(s - a)(s - b)(s - c)

[Where, S is semi-perimeter and a, b, c are sides of triangle].

• Semi-perimeter = Perimeter of triangle/2.

• Perimeter of triangle = Sum of all sides.

• Area of parallelogram = Base × height.

____

So,

⇒s = 26 + 37 + 28/2

⇒ s = 91/2

Semi-perimeter is 91/2 cm.

Area of triangle :

$\longrightarrow \sf \sqrt{\dfrac{91}{2} \times \bigg( \dfrac{91}{2} - 26\bigg) \times \bigg( \dfrac{91}{2} - 37\bigg) \times \bigg( \dfrac{91}{2} - 28\bigg)}$

$\longrightarrow \sf \sqrt{\dfrac{91}{2} \times \bigg( \dfrac{91-52}{2} \bigg) \times \bigg( \dfrac{91-74}{2} \bigg) \times \bigg( \dfrac{91-56}{2} \bigg)}$

$\longrightarrow \sf \sqrt{\dfrac{91}{2} \times \dfrac{39}{2} \times \dfrac{17}{2} \times \dfrac{35}{2}}$

$\longrightarrow \sf \sqrt{45.5 \times 19.5 \times 8.5 \times 17.5}$

$\longrightarrow \sf \sqrt{131978.438}$

$\longrightarrow \pmb{\sf 363.289}$

Area of triangle is 363.289 cm².

Area of triangle = Area of parallelogram

Area of parallelogram = 363.289 cm²

Now,

→ Base × height = 363.289

→ 28 × height = 363.289

→ Height = 363.289/2

→ Height = 12.98

∴ Height of parallelogram is 12.98 cm.