Question

In the given figure, ABCD is a rectangle in which diag. AC = 17 cm, ∠BCA = θ and `sin θ = 8/17`.

Find (i) the area of rect. ABCD,

(ii) the perimeter of rect. ABCD.

Answer 1

`sin θ = 8/17`

⇒ `(AB)/(AC) = 8/17`

∴ AB = 8 cm.

In right ΔABC, we have

BC² = (AC² – AB²)

= {(17)² – 8²} cm²

= (289 – 64) cm²

= 225 cm²

⇒ `BC = sqrt(225)  cm`

⇒ BC = 15 cm

∴ `l` = 15 cm and b = 8 cm.

(i) Area of rect. ABCD = (15 × 8) cm² 

= 120 cm²

(ii) Perimeter of rect. ABCD = 2(`l` + b) 

= 2(15 + 8) cm 

= 46 cm