Question

The perimeter of an isosceles triangle is $42cm$ and its base is $1\frac{1}{2}$ 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, $\sqrt{7}=\mathrm{2.64.}$)

Answer 1

(i)

the length of each side of the triangle

$1\frac{1}{2}x+x+x=42$

$\frac{3}{2}x+x+x=42$

$\frac{7}{2}x=42$

$x=12$cm

$side=12$cm

(iii)

the height of the triangle

$bas{e}^2+heigh{t}^2=hypotenus{e}^2$

$\Rightarrow heigh{t}^2={12}^2-9^2=63$

$\therefore height=\sqrt{63}=3\sqrt{7}$cm

(ii)

Area of the triangle

Area$=\frac{1}{2}base\times height$

$=\frac{1}{2}\times 18\times 3\sqrt{7}$

$=71.28$sq units