The base of an isosceles triangle is 6 cm and each of its equal sides is 5 cm.

Question:

The base of an isosceles triangle is 6 cm and each of its equal sides is 5 cm. The height of the triangle is

(a) 8 cm

(b) $\sqrt{30} \mathrm{~cm}$

(c) $4 \mathrm{~cm}$

(d) $\sqrt{11} \mathrm{~cm}$

Solution:

(c) 4 cm

Height of isosceles triangle $=\frac{1}{2} \sqrt{4 a^{2}-b^{2}}$

$=\frac{1}{2} \sqrt{4(5)^{2}-6^{2}} \quad(a=5 \mathrm{~cm}$ and $b=6 \mathrm{~cm})$

$=\frac{1}{2} \times \sqrt{100-36}$

$=\frac{1}{2} \times \sqrt{64}$

$=\frac{1}{2} \times 8$

$=4 \mathrm{~cm}$

 

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