Question

the perimeter of an isosceles triangle is 42 cm and its base is 3 times each of the equal side find (1) the length of each side of the triangle (2) the area of the triangle and (3)the height of the triangle . (given √7=2.64 )​

Answer 1

CORRECT QUESTION.

The perimeter of an isosceles triangle is 42 CM

and it's base is 3/2 times each of the equal

sides. find (1) the length of each sides of the

triangle (2) the area of the triangle (3) the

height of the triangle ( given = √7 = 2.64 )

EXPLANATION.

$\sf : \implies \: let \: the \: measure \: of \: each \: equal \: sides \: = x \\ \\ \sf : \implies \: x + x + \frac{3x}{2} = 42 \\ \\ \sf : \implies \: \frac{7x}{2} = 42 \\ \\ \sf : \implies \: x = 12 \: cm$

$\sf : \implies \: its \: sides \: are \: \\ \\ \sf : \implies \: x = 12 \: cm \\ \\ \sf : \implies \: x \: = 12 \: cm \\ \\ \sf : \implies \: \frac{3x}{2} = \frac{3 \times 12}{2} = 18 \: cm$

$\sf : \implies \: s \: = \dfrac{a + b + c}{2} \\ \\ \sf : \implies \: s \: = \frac{12 + 12 + 18}{2} = \frac{42}{2} = 21 \: cm$

$\sf : \implies \: by \: using \: herons \: formula \: \\ \\ \sf : \implies \: \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sf : \implies \: \sqrt{21(21 - 12)(21 - 12)(21 - 18)} \\ \\ \sf : \implies \: \sqrt{21 \times 9 \times 9 \times 3} \\ \\ \sf : \implies \: \sqrt{5103} = 71.42 \: cm {}^{2}$

$\sf : \implies \: area \: of \: triangle \: = 71.42 \: cm {}^{2} \\ \\ \sf : \implies \: \frac{1}{2} \times 18 \times h = 71.42 \\ \\ \sf : \implies \: h \: = \frac{71.42 \times 2}{18} \\ \\ \sf : \implies \: h \: = 7.937 \: cm$

$\sf : \implies \: \green{{ \underline{1) = the \: length \: of \: each \: sides \: of \: triangle\: 12,12,18}}} \\ \\ \sf : \implies \green{{ \underline{2) = area \: of \: the \: triangle \: = 71.42cm {}^{2} }}} \\ \\ \sf : \implies \: \green{{ \underline{3) = height \: of \: the \: triangle \: = 7.937 \: cm}}}$