Question

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step- by -step​

Answer 1

$\bold{\underline{\underline{\huge{\sf{ANSWER\::}}}}}$

Given:

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26cm,28cm & 30cm, and the parallelogram stands on the base 28cm.

To find:

The height of the parallelogram.

Explanation:

Given,

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

Area of parallelogram = area of the triangle.

We know that formula of area of the parallelogram: Base× Height  

We know that area of the triangle: √(s-a)(s-b)(s-c)

• Using Heron's Formula:

s is the semi-perimeter of the triangle.

a,b,c are the sides of the triangle.

We have,

• a= 26cm
• b= 28cm
• c= 30cm

→ $s=\:\frac{a+b+c}{2}$

→ $s=\:(\frac{26+28+30}{2} )cm$

→ $s=\:\cancel{(\frac{84}{2} )}cm$

→ s = 42cm

&

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

Area of triangle= $\sqrt{42(42-26)(42-28)(42-30)} cm^{2}$

Area of triangle= $\sqrt{42(16)(14)(12)} cm^{2}$

Area of triangle= $\sqrt{2*3*7*2*2*2*2*2*7*2*2*3} cm^{2}$

Area of triangle= (2×2×2×2×3×7)cm²

Area of triangle= 336cm²

Now,

→ Area of parallelogram = area of triangle

→ Base × Height = 336cm²

→ 28cm × Height = 336cm²

→ Height= $\cancel{\frac{336cm^{2} }{28cm} }$

→ Height= 12cm.

Thus,

The height of the parallelogram is 12cm.

Answer 2

Answer:

triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26cm,28cm & 30cm, and the parallelogram stands on the base 28cm.

To find:

The height of the parallelogram.

Explanation:

Given,

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

Area of parallelogram = area of the triangle.

We know that formula of area of the parallelogram: Base× Height

We know that area of the triangle: √(s-a)(s-b)(s-c)

Using Heron's Formula:

s is the semi-perimeter of the triangle.

a,b,c are the sides of the triangle.

We have,

a= 26cm

b= 28cm

c= 30cm

→ s=\:\frac{a+b+c}{2}s=

2

a+b+c

→ s=\:(\frac{26+28+30}{2} )cms=(

2

26+28+30

)cm

→ s=\:\cancel{(\frac{84}{2} )}cms=

(

2

84

)

cm

→ s = 42cm

&

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

s(s−a)(s−b)(s−c)

Area of triangle= \sqrt{42(42-26)(42-28)(42-30)} cm^{2}

42(42−26)(42−28)(42−30)

cm

2

Area of triangle= \sqrt{42(16)(14)(12)} cm^{2}

42(16)(14)(12)

cm

2

Area of triangle= \sqrt{2*3*7*2*2*2*2*2*7*2*2*3} cm^{2}

2∗3∗7∗2∗2∗2∗2∗2∗7∗2∗2∗3

cm

2

Area of triangle= (2×2×2×2×3×7)cm²

Area of triangle= 336cm²

Now,

→ Area of parallelogram = area of triangle

→ Base × Height = 336cm²

→ 28cm × Height = 336cm²

→ Height= \cancel{\frac{336cm^{2} }{28cm} }

28cm

336cm

2

→ Height= 12cm.

Thus,

The height of the parallelogram is 12cm

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