1.

The perimeter of an isosceles triangle is 42 cm and its base is `1(1)/(2)` times each of the equal sides. Find (i) the length of each side of the triangle, (ii) the area of the triangle, and (iii) the height of the triangle. (Given, `sqrt(7) = 2.64`.)

Answer» Correct Answer - (i) 12 cm, 12 cm, 18 cm (ii) 71.28 `cm^(2)` (iii) 7.92 cm
(i) `x + x + (3)/(2)x = 42 rArr (7x)/(2) = 42 rArr x = (84)/(7)=12`.
So, the sides are 12 cm, 12 cm, 18 cm.
(ii) Area of the triangle `= sqrt(s(s-a)(s-b)(s-c))=sqrt(21 xx 9 xx 9 xx 3)cm^(2)`
`" "=(27 xx sqrt(7))cm^(2)=(27 xx 2.64)cm^(2)=71.28 cm^(2)`.
(iii) `(1)/(2) xx 18 cm xx h = 71.28 cm^(2) rArr h=(71.28)/(9)cm = 7.92 cm`.


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