Question

Find: (1) the area of triangle whose three sides are 8 cm, 15cm, and 17 cm (2) the altitude from the opposite vertex to the side whose length is 15 cm.

Answer 1

this can be done using heron's formula
s=(8+15+17)/2=40/2
=20

$\sqrt{s(s - 1)(s - 2)(s - 3)}$

√20*(20-8)(20-15)(20-17)
√20*12*5*3
√3600
=60cm²



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Answer 2

Hola

Answer -

Given - Sides of Triangle ABC

8cm, 17cm, 15cm


To find - 1) Area of the given Triangle

2) The measure of the altitude AD


Calculation -

Area of triangle = √ s ( s - a) (s - b) ( s- c)

First, We will find S


s = a + b + c / 2

s = 8 + 15 + 17 / 2

= 40/2 => 20

Therefore,

√20 ( 20 - 8) ( 20 - 15) ( 20 - 17)


= √ 20 ( 12) (5) (3)


= √ 2 × 5 × 2 × 4 × 3 × 5 × 3


= 2 × 5 × 3 × 2


= 10 × 6


= 60cm²


Therefore, Area of Triangle = 60cm²

We know that the Altitude is perpendicular from the base to its opposite vertex.

Hence, We can find the length of Vertex by the Pythagoras Thereom.

Therefore,

In ∆ABD

(AB)² = (BD)² + (AD)²

AD is 1/2 AC

Therefore,

(8)² = (BD)² + (7.5)²

64 = (BD)² + 56.25

(BD)² = 64 - 56.25

(BD)² = 11.5

BD = √11.5

Hope it helps