Question

28. Find the area of the triangle ABD in the diagram below.​

Answer 1

Step-by-step explanation IN triangle abc,

AC² = AB² + BC² (Phythogoras theorem)

13² = 5² + BC²

169 - 25 = BC²

144 = BC²

BC² = 144

BC = 12 (APPLAYING SQAURE ROOT)

Then in triangle ADC,

AD² = AC² + CD²

AD² = 13² + 12² (CD = BD - BC)

AD² = 169 + 144

AD = 17cm (aprox.)

Therefore area of triangle abd = 1/2× length × side = 1/2× 5 ×24 = 5 × 12 = 60cm

Answer 2

A = 60 cm²

Explanation:

Finding BC using Pythagorean Theorem:

=>
`c^2= a^2+b^2`

=>
`13^2 = a^2+5^2`

=> 169-25 =
`a^2`

=>
`a^2` = 144

Taking sqrt on both sides

=> BC = 12

So,

BC = CD = 12

=> BD = BC+CD

=> BD = 12+12

=> BD = 24

Now, The area:

=> Area of a Triangle =
`(1)/(2) (Base)(Height)`

Where BASE = 24, HEIGHT = 5

=> A = 1/2(5)(24)

=> A = 1/2(120)

=> A = 60 cm²