Question

14. Find the area of the triangle in which two sides are 8 cm and 11 cm and the perimeter is 32 cm.​

Answer 1

Answer:

6588

Step-by-step explanation:

In the PQR, S and T are points on sides PQ and PR respectively such that

ST||QR. If PT = 1 cm; PS=1.5 cm and SQ=3 cm, th

Answer 2

$\Large{\underbrace{\sf{\pink{Required\:Solution:}}}}$

Given thαt,

• Two sides of α triαngle αre 8cm αnd 11cm.
• The perimeter is 32cm.

◾️We need to find the αreα of the triαngle.

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To do so,

Let's αssume the third side to be x.

According to the question,

:$\implies{\sf{ 8cm + 11cm + x = 32cm}}$

:$\implies{\sf{ 19cm + x = 32cm}}$

:$\implies{\sf{ x = 32cm-19cm}}$

:$\implies{\sf{ x = 32cm-19cm}}$

:$\implies{\sf{ x = 13cm}}$

Hence, the length of the third side is 3cm.

Heron's Formulαe -

$\large\star{\boxed{\sf{\pink{ Area_{(triangle)} = \sqrt{s(s-a)(s-b)(s-c)}}}}}$

Where, s = semiperimeter αnd a,b αnd c = sides.

:$\implies{\sf{ semiperimeter = \dfrac{a+b+c}{2}}}$

• Substitute the vαlues αnd simplify.

:$\implies{\sf{ semiperimeter = \dfrac{11cm+8cm+13cm}{2}}}$

:$\implies{\sf{ \dfrac{32cm}{2}}}$

:$\implies{\sf{16cm}}$

• Substitute the vαlues in heron's formulαe αnd simplify.

:$\implies{\sf{ \sqrt{16(16-8)(16-11)(16-3)}}}$

:$\implies{\sf{ \sqrt{16(8)(5)(13)}}}$

:$\implies{\sf{ \sqrt{ 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 13}}}$

:$\implies{\sf{ 2\times 2\times 2 \sqrt{ 2 \times 5 \times 13}}}$

:$\large\implies{\boxed{\sf{\pink{ 8\sqrt{ 130}cm}}}}$

Hence, the αreα of the triαngle is 8√130cm.

And we αre done! :D

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