Question

Find the area of a triangle whose sides are 34cm ,20cm,and42cm.Hence ,find the length of the altitude corresponding to the shortest side
(Pls give the ansure correct )

Answer 1

Area of the triangle is 336 sq cm. and the length of the altitude to the shortest side is 33.6 cm.

• The area of the triangle when all sides are given is calculated by Heron's formula

Area =$\sqrt{S(S-A)(S-B)(S-C)}$

where S =$\frac{A+B+C}{2}$(semi-perimeter)

and A,B,C are sides of the triangle.

• We calculate S = $\frac{34+20+42}{2}$

S = 48 cm

• Now A = $\sqrt{48(48 -34)(48-20)(48-42)}$

A = 336 sq cm.

• Now we have to find the length of the altitude to the shortest side, the shortest side is 20 cm.
• We have other formulas to calculate area one of which is $\frac{1}{2}$ × base × height
• Now we assume the base to be the shortest one , using the above formula we will get to know the altitude's length to the shortest side.
• We substitute the known values,

336 = (1/2) × 20 × height(altitude)

height = 33.6 cm

• The altitude's length is 33.6 cm and area is 336 sq. cm.