Question

In the adjoining diagram, AB = x cm, BC = у cm and x – y = 7 cm. Area of ΔABC = 30 cm². The length of AC is:

Options

• 10 cm

• 12 cm

• 13 cm

• 15 cm

Answer 1

13 cm

Explanation:

Right triangle with legs x and y gives area

`1/2 xx x xx y = 30` 

⇒ x × y = 60

Also x – y = 7

⇒ (x – y)² = 49 

= x² + y² – 2xy

So, x² + y² = 49 + 2 × 60 

= 169 

Hence, `AC = sqrt(x^2 + y^2)`

= `sqrt(169)`

= 13 cm