Question

pls ans fast fast .. its a humble request frnds ​

Answer 1

Given

• Base of the isosceles triangle is 24cm.
• Area of the isosceles triangle is 192 cm².

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To find

• Perimeter of the triangle.

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Solution

• We have base and area of the triangle.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{We\: know\: that}}}$

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$\large{\boxed{\boxed{\bf{Area_{(Triangle)} = \dfrac{1}{2} \times base \times height}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {192 = \dfrac{1}{2} \times 24 \times height}$

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$\tt:\implies\: \: \: \: \: \: \: \: {192 = 12 \times height}$

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$\tt:\implies\: \: \: \: \: \: \: \: {height = \dfrac{192}{12}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {height = 16\: cm}$

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• Now, as shown in the figure DC = 12cm

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★ ∆ADC is a right angled triangle

[Using Pythagoras theorem]

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$\tt:\implies\: \: \: \: \: \: \: \: {AC^2 = AD^2 + DC^2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {AC^2 = (16)^2 + (12)^2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {AC^2 = 256 + 144}$

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$\tt:\implies\: \: \: \: \: \: \: \: {AC^2 = 400}$

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$\tt:\implies\: \: \: \: \: \: \: \: {AC = \sqrt{400}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {AC = 20}$

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• Two sides of a isosceles triangle are equal, AB = AC = 20cm.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Perimeter\: of\: isosceles\: triangle\: is\: given\: by}}}$

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$\large{\boxed{\boxed{\bf{Perimeter_{(Isosceles\: triangle)} = 2(side) + base}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Perimeter = 2(20) + 24}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Perimeter = 40 + 24}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Perimeter = 64\: cm}$

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Hence,

• The perimeter of the isosceles triangle is 64cm.

Answer 2

Given⠀

Base of the isosceles triangle is 24cm.

Area of the isosceles triangle is 192 cm².

To find

Perimeter of the triangle.

Solution

We have base and area of the triangle.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{We\: know\: that}}}$

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$\large{\boxed{\boxed{\bf{Area_{(Triangle)} = \dfrac{1}{2} \times base \times height}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {192 = \dfrac{1}{2} \times 24 \times height}$

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