The sides of a triangle are 45 cm, 60 cm and 75 cm. The length of the altitude drawn to the longest side from its

Q: The sides of a triangle are 45 cm, 60 cm and 75 cm. The length of the altitude drawn to the longest side from its opposite vertex is

(d) 36 cm Let $s$ be the semi-perimeter of the triangle. Then, $2 s=(45+60+75) cm \Rightarrow s=90$ Let $A$ be the area of the triangle. Then, $\begin{array}{l}\quad A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{90(90-45)(90-60)(90-75)} \\ \Rightarrow \quad A=\sqrt{90 \times 45 \times 30 \times 15}=\sqrt{2 \times 3^2 \times 5 \times 3^2 \times 5 \times 3 \times 2 \times 5 \times 3 \times 5}=2 \times 3^3 \times 5^2 cm^2=1350 cm^2 \\ Also, \quad A=\frac{1}{2}(75 \times \text { Altitude drawn to the longest side }) \\ \Rightarrow \quad 1350=\frac{1}{2} \times 75 \times \text { Altitude drawn to the longest side } \\ \Rightarrow \quad \text { Altitude drawn to the longest side }=36 cm .\end{array}$

M.C.Q

CBSE - English Medium

The sides of a triangle are 45 cm, 60 cm and 75 cm. The length of the altitude drawn to the longest side from its opposite vertex is

A
27 cm
B
21 cm
C
39 cm
D
36 cm

STD 9
Maths
Herons Formula
RD Sharma

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