Question

19. The difference between the sides at right
angles in a right angled triangle is 14 cm.
The area of the triangle is 120 cm. The
perimeter of the triangle is
(a) 68 cm
(b) 64 cm
(C) 60 сm
(d) 58 cm​

Answer 1

Answer:

C) 60 cm

Step-by-step explanation:

area of triangle = 1/2 × b × h = 120

let base be x and height be (x - 14)

$120 = \frac{1}{2} \times x \times (x - 14) \\ 120 \times 2 = {x}^{2} - 14x \\ 240 = {x}^{2} - 14x \\ {x}^{2} - 14x - 240 = 0 \\ {x}^{2} - 24x + 10x - 240 = 0 \\ x(x - 24) + 10(x - 24) = 0 \\ (x - 24)(x + 10) = 0 \\ x - 24 = 0 \: \: \: \: x + 10 = 0 \\ x = 24 \: \: \: \: \: \: \: x = - 10$

we get one side as x = 24

other side = x - 14 = 24 - 14 = 10

using Pythagoras theorem

${hyp}^{2} = {base}^{2} + {height}^{2} \\ {hyp}^{2} = {24}^{2} + {10}^{2} \\ = 576 + 100 \\ = 676 \\ {hyp}^{2} = 676 \\ hyp = \sqrt{676} \\ hyp = 26$

perimeter of triangle

= 24 + 10 + 26

= 60 cm

hope you get your answer