Question

find the area of the isosceles triangle whose base is 3 cm and perimeter 8 cm

Answer 1

hope it will help you

Answer 2

$\huge\bold\blue{Solution :\longrightarrow}$

$\mathsf\red{Let \: \: each \: \: of \: \: the \: \: equal \: \: sides \: \: be \: \: a \: \: cm.}$

$\mathsf\red{Then, \: \: a + a + 3 = 8}$

$\mathsf\red{ = > 2a = 8 - 3}$

$\mathsf\red{= > 2a = 5}$

$\mathsf\red{ = > a = \frac{5}{2}}$

$\mathsf\red{ = > a = 2.5}$

$\mathsf\purple{Therefore, \: \: b = 3 \: cm \: \: and \: \: a = 2.5 \: cm.}$

$\mathsf\green{area \: \: of \: \: the \: isosceles \: \: triangle}$

$\mathsf\green{ = \frac{1}{2} \times b \times \sqrt{a {}^{2} - \frac{ {b}^{2} }{4} }}$

$\mathfrak\green{= [\frac{1}{2} \times 3 \times \sqrt{ {2.5}^{2} - \frac{ {3}^{2} }{4} } \:] \: \: {cm}^{2}}$

$\mathfrak\green{ = [\frac{3}{2} \times \sqrt{6.25 - \frac{9}{4} } \: \: ]\: {cm}^{2}}$

$\mathfrak\green{ = (1.5 \times \sqrt{6.25 - 2.25} ) \: \: {cm}^{2}}$

$\mathfrak\green{ = (1.5 \times \sqrt{4} ) \: \: {cm}^{2}}$

$\mathfrak\green{ = (1.5 \times 2) \: \: {cm}^{2}}$

$\mathfrak\green{ = 3 \: \: {cm}^{2}} \: \: \:\bold{\boxed{\boxed{\boxed{\blue{ Ans}}}}}$

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