Use the information given in the given figure to find:

(i) the length of AC.

(ii) the area of △ ABC.

(iii) the length of BD, correct to one decimal place.

(i) Given:

In triangle ABC,

Base of the triangle = 24 cm

Height of the triangle = 7 cm

Let h be the hypotenuse of the triangle.

In a right-angled triangle, using the Pythagorean theorem,

Base² + Height² = Hypotenuse²

⇒ (24)² + (7)² = h²

⇒ 576 + 49 = h²

⇒ h² = 625

⇒ h = $\sqrt{625}$

⇒ h = 25 cm

Hence, the length of AC = 25 cm.

(ii) As we know, the area of a triangle = $\dfrac{1}{2}$ x side x height

= $\dfrac{1}{2}$ x 24 x 7 cm²

= $\dfrac{1}{2}$ x 168 cm²

= 84 cm²

Hence, the area of the triangle = 84 cm².

(iii) The base of the triangle = 25 cm

Let the height of the triangle be h.

As we know, the area of a triangle = $\dfrac{1}{2}$ x side x height

[∵ Both areas remain same since they represent the area of the same triangle.]

⇒ $\dfrac{1}{2}$ x 25 x h = 84

⇒ 25 x h = 2 x 84

⇒ 25 x h = 168

⇒ h = $\dfrac{168}{25}$

⇒ h = 6.7 cm

Hence, the length of BD = 6.7 cm.