Question

# The perimeter of an isosceles triangle is 42 cm and its base is $\left(\frac{3}{2}\right)$ times each of the equal sides. Find the length of each side and area of the triangle.

Open in App
Solution

## Let a, b and c be the sides of the triangle. Here, a = b and $c\left(\mathrm{base}\right)=\frac{3}{2}a$. Since the perimeter of the triangle is 42 cm, so $a+b+c=42\phantom{\rule{0ex}{0ex}}⇒a+a+\frac{3}{2}a=42\phantom{\rule{0ex}{0ex}}⇒a=12\mathrm{cm}\phantom{\rule{0ex}{0ex}}⇒c=\frac{3}{2}×a=\frac{3}{2}×12=18\mathrm{cm}$ Therefore, the lengths of the sides of the triangle are 12 cm, 12 cm and 18 cm. Now $s=\frac{a+b+c}{2}=\frac{12+12+18}{2}=21\mathrm{cm}\phantom{\rule{0ex}{0ex}}\mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\phantom{\rule{0ex}{0ex}}=\sqrt{21\left(21-12\right)\left(21-12\right)\left(21-18\right)}\phantom{\rule{0ex}{0ex}}=\sqrt{21\left(9\right)\left(9\right)\left(3\right)}=27\sqrt{7}{\mathrm{cm}}^{2}$ Hence, the area of the triangle is $27\sqrt{7}{\mathrm{cm}}^{2}$.

Suggest Corrections
0
Related Videos
Area of an Equilateral Triangle
MATHEMATICS
Watch in App