Question

In the figure, ABC is a right angled triangle,find

(i) The area of ABC
(ii) the length of BD correct to two places of decimal ​

Answer 1

Answer:

(1). The area of the triangle A = 180  

(2). The length of AC is = 41 cm

(3). The length of BD = 8.78 cm

Step-by-step explanation:

Given data

AB = 9 cm

BC = 40 cm

Since ABC is a right angle triangle.So

(1). Area of the triangle  is = 0.5 × AB × BC

⇒ A = 0.5 × 9 × 40

⇒ A = 180  

Therefore the area of the triangle A = 180  

(2). From pythagoras theorm

AC = 41 cm

Therefore the length of AC is = 41 cm

(3). Let AD = x & CD = 41 - x

From Δ ABD

 ------- (1)

From Δ BDC

 ------- (2)

Equation 1 = Equation 2

⇒  

⇒  

⇒ x = 1.976 cm

We know that x = AD = 1.976 cm

Put the value of x in equation 1 we get

 = 77.095

BD = 8.78 cm

Therefore the length of BD = 8.78 cm

Answer 2

(i) The area of ABC = 180cm²

(ii) the length of BD correct to two places of decimal = 8.78 cm

Step-by-step explanation:

(i) The area of ABC

$= \frac{1}{2} \times bc \times ab$

$= \frac{1}{2} \times 40 \times 9$

= 20 × 9

= 180 cm²

Now, AC² = AB² + BC²

AC²= 81 + 1600 = 1681

AC = Square root 1681

AC = 41 cm

The area of ABC = 180 cm²

1/2 × AC × BD = 180

1/2 × 41 × BD = 180

BD = (180 ×2) ÷ 41

BD = 360 ÷ 41

BD = 8.7804 = 8.78 cm (upto 2 Decimals)