Question

The perimeter of an isosceles triangle is 44 cm and ratio of the equal side to its base is 4 : 3. The area of the triangle is:​

Answer 1

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Required Answèr :

$\underline{\boxed{\large\rm{Area = 88.99\:cm^{2} }}}$

Given:-

Perimeter of the isosceles triangle = 44 cm.

Ratio of it's side and base = 4:3 = 4/3

To Find:-

Area of the triangle.

Solution:-

An isosceles triangle has two equal sides.

So,

Let the two equal side be 4x.

Let the base be 3x.

Then,

$\sf\underline{\boxed{\large{\mathfrak{perimeter = side + base}}}}$

$\rm { : \implies \: \: 4x + 4x + 3 x=44}$

$\rm { : \implies \: \: 8x+3x=44}$

$\rm { : \implies \: \: 11x=44}$

$\rm { : \implies \: \: x= \dfrac{44}{11} }$

$\rm:\implies \underline{\boxed{\pink{\mathfrak{x = 4}}}}\:\:\star$

Therefore,

➼ Side (a) = 4 × 4 = 16 cm

➼ Side (b) = 4 × 4 = 16 cm

➼ Base (c) = 3 × 4 = 12

Now,

$\rm { : \implies \: \: s=\dfrac{a+b+c}{2} }$

$\rm { : \implies \: \: s=\dfrac{16+16+12}{2} }$

$\rm { : \implies \: \: s=\dfrac{32+12}{2} }$

$\rm { : \implies \: \: s=\dfrac{44}{2} }$

$\rm:\implies \underline{\boxed{\blue{\mathfrak{s=22}}}}\:\:\star$

Formula to find the area :-

$\sf\underline{\boxed{\large{\mathfrak{ \sqrt{s(s-a)(s-b)(s-c)} }}}}$

$\rm { : \implies \: \: \sqrt{22(22-16)(22-16)(22-12)} }$

$\rm { : \implies \: \: \sqrt{22 \times(6)\times(6)\times(10)} }$

$\rm { : \implies \: \: \sqrt{2\times11\times6\times6\times2\times5} }$

$\rm { : \implies \: \: 2 \times6 \sqrt{11\times5} }$

$\rm { : \implies \: \: 12\sqrt{55} }$

$\rm:\implies \underline{\boxed{\purple{\mathfrak{88.99\:cm^{2} }}}}\:\:\bigstar$

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Answer 2

Answer:

Answer is 88.99 cm²

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