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 30 cm, find the height of the
parallelogram. ​

Answer 1

AnswEr :

• Sides of Triangle are 26cm, 28cm and 30cm.
• Base of Parallelogram is 30cm.
• Area of Both Shape is Same.
• Find Height of Parallelogram.

• A R E A ⠀O F ⠀T R I A N G L E :

$\longrightarrow \tt Semi \:Perimeter (s) = \frac{a + b + c}{2} \\ \longrightarrow \tt s = \frac{(26 + 28 + 30)}{2} \\ \longrightarrow \tt s = \cancel\frac{84}{2} \\ \longrightarrow \tt s = 42$

$\implies \blue{\tt Area_{\tiny Triangle} = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ \implies\tt Area_{\tiny Triangle} = \sqrt{42(42 - 26)(42 - 28)(42 - 30)} \\ \\ \implies\tt Area_{\tiny Triangle} = \sqrt{42 \times 16 \times 14 \times 12} \\ \\ \implies\tt Area_{\tiny Triangle} = \sqrt{(7 \times 6) \times (4 \times 4) \times (7 \times 2) \times (6 \times 2)} \\ \\ \implies\tt Area_{\tiny Triangle} =7 \times 6 \times 4 \times 2 \\ \\ \implies \boxed{\tt Area_{\tiny Triangle} =336 \: {cm}^{2}}$

$\rule{300}{2}$

• According to the Question Now :

$\mapsto \tt Area_{\tiny Triangle} = Area_{\tiny Parallelogram} \\ \\ \mapsto \tt Area_{\tiny Triangle} = Base \times Height \\ \\ \mapsto \tt336 {cm}^{2} = 30cm\times Height \\ \\ \mapsto \tt \frac{336}{30} = Height \\ \\ \mapsto \large\boxed{\red{\tt Height = 11.2 \:cm}}$

⠀

∴ Height of the Parallelogram is 11.2 cm

Answer 2

Solution:-

Given that:-

• A triangle and a parallelogram have the same base and the same area.

• Sides of the triangle are 26 cm, 28 cm and 30 cm

• parallelogram stands on the base 30 cm

To find:-

• Height of the parallelogram

_______________________________________

Area of parallelogram = area of triangle

Base × height = area of triangle

30 × height = area of triangle

Height = $\frac{1}{30}$ × area of triangle.

Area of triangle:-

$\sqrt[]{s(s - a)(s - b)(s - c)}$

S = semi perimeter

ABC = Sides of triangle.

A = 26

B = 30

C = 28

$s = \frac{a + b + c}{2} = \frac{26 + 28 + 30}{2} \\ \\ = \frac{84}{2} = 42m$

$\sqrt[]{42(42 - 26)(42- 28)(42 - 30)cm {}^{2} }$

$\sqrt[]{42(16)(14)(12)}$

$\sqrt[]{(14 \times 3) \times (16) \times (14) \times (12)}$

$\sqrt[]{(14 \times 14) \times (12 \times 3) \times (16)}$

$\sqrt[]{(14 {}^{2}) \times (36) \times (16) }$

$\sqrt[]{(14 {}^{2}) \times (6 {}^{2} ) \times (4 {}^{2} ) }$

$\sqrt[]{(14 ){}^{2} } \times \sqrt[]{(6) {}^{2} } \times \sqrt[]{(4) {}^{2} }$

= 14 × 6 × 4

= 336

Area of triangle = 336

Now,

Height= $\frac{1}{30}$ × area of triangle.

= $\frac{1}{30}$ × 336 = 11.2

•°• Height of parallelogram = 11.2cm.