Question

lugu
Calculate the area of the triangle whose sides are 18 cm, 24 cm and
30 cm in length. Also, find the length of the altitude corresponding to
the smallest side.​

Answer 1

Answer:

The ‘area of triangle’ is 216 and ‘Altitude’ = 24 cm

To find:

‘Area of triangle’ & ‘length of the altitude’ corresponding to the ‘smallest side’.

Solution:

Given: Sides are 18 cm, 24 cm and 30 cm in length.

Firstly, we need to find s i.e., half of the triangles perimeter

S=\frac{a+b+c}{2}S=

2

a+b+c

whereas a, b & c are three sides of triangle.

\begin{lgathered}\begin{array}{l}{=\frac{18+24+30}{2}} \\ \\ {=\frac{72}{2}} \\ \\ {=36}\end{array}\end{lgathered}

=

2

18+24+30

=

2

72

=36

Secondly, the formula for ‘area of triangle’ is

\sqrt{s(s-a)(s-b)(s-c)}

s(s−a)(s−b)(s−c)

=\sqrt{36(36-18)(36-24)(36-30)}=

36(36−18)(36−24)(36−30)

=\sqrt{36 \times 18 \times 12 \times 6}=

36×18×12×6

=\sqrt{6 \times 6 \times 3 \times 6 \times 2 \times 6 \times 2 \times 3}=

6×6×3×6×2×6×2×3

=\sqrt{2 \times 3 \times 2 \times 3 \times 3 \times 2 \times 3 \times 2 \times 2 \times 3 \times 2 \times 3}=

2×3×2×3×3×2×3×2×2×3×2×3

=2 \times 2 \times 2 \times 3 \times 3 \times 3=2×2×2×3×3×3

=216\ \mathrm{cm}^{2}=216 cm

2

Thirdly, shortest side = 18 cm

Area of triangle = 216

\begin{lgathered}\begin{array}{l}{\frac{1}{2} \times \text { base } \times \text { altitude }=216} \\ \\ {\frac{1}{2} \times 18 \times \text { altitude }=216}\end{array}\end{lgathered}

2

1

× base × altitude =216

2

1

×18× altitude =216

9 \times \text { altitude }=2169× altitude =216

Hence, Altitude = 24 cm i.e. corresponding to shortest side.