Question

The length of the sides of a trangle are 13cm,14cm
and 15 cm Find the length of the attitude corresponding
to longest side​

Answer 1

Given:

• Length of first side of triangle = 13cm

• Length of second side of triangle = 14cm

• Length of third side of triangle = 15cm

To Find:

• Length of attitude corresponding to longest side 15 cm.

Solution:

➥ Finding area of triangle:

Here,

First Side = a = 13cm

Second Side = b = 14cm

Third Side = c = 15cm

Value of s = Perimeter ÷ 2

= (13+14+15) ÷ 2

= 42 ÷ 2

= 21

Area of ∆ by Heron's Formula

√s (s-a) (s-b) (s-c)

= √21 (21-13) (21-14) (21-15)

= √21 × 8 × 7 × 6

= √ 7 × 3 × 2 × 2 × 2 × 7 × 3 × 2

= 7 × 3 × 2 × 2

= 21 × 4

= 84 cm²

➥ Finding altitude of triangle with base 15cm.

According to above answer;

Area of triangle = 84cm²

➨ ½ × base × height = 84

➨ ½ × 15 × height = 84

➨ 15 × height = 84 ÷ 2

➨ height = 42 ÷ 15

➨ height = 2.8

∴ Height = 2.8cm

Answer:-

• Length of attitude corresponding to longest side (15 cm) is 2.8 cm.

Formula to be remembered:-

▪︎Area of square = Side × Side

▪︎Area of rectangle = length × breadth

▪︎Area of triangle = ½ × Base × Height

or

By Heron's Formula

▪︎Area of trapezium = ½(Sum of parallel sides) × Height

Answer 2

Area of triangle with sides a, b, and c and

s=

2

a+b+c

is

s(s−a)(s−b)(s−c)

.

For triangle with sides 13 cm, 14 cm and 15 cm,

s=

2

13+14+15

=

21cm

∴ Area of the triangle with sides 13 cm, 14 cm and 15 cm,

=

21(21−13)(21−14)(21−15)

=

21×8×7×6

=

7×3×2×4×7×2×3

= 7× 3× 2× 2= 84

cm