Question

In Angle ABC; angleA = 90°, side AB = x cm, AC = (x+5) cm and area =150cm²
Find the sides of the triangle.​

Answer 1

Answer:

15,20,25

Step-by-step explanation:

1/2×(x+5)×x=150

x²+5x-300=0

x²+20x-15x-300=0

x(x+20)-15(x+20)=0

(x+20)(x-15)=0

x=15

AB=15cm

Ac=20cm

BC²=15²+20²

BC=25cm

Answer 2

Step-by-step explanation:

angle A = 90

side AB = X cm

side Ac = x+5

area = 150 sq.cm

area of right angled triangle = 1/2 × AB × AC

150 = 1/ 2 × x × ( x+ 5 )

150 ×2 = x ^2 + 5x

300 =x^2 +5x

${x}^{2} + 5x - 300 = 0$

${x}^{2} - 15x + 20x - 300 = 0$

$x(x - 15) + 20(x - 15) = 0$

$(x - 15)(x + 20) = 0$

x-15 = 0 or x+20 = 0

x= 15 or x = -20

length of the side is not negative

x = 15

x+5 = 20

by Pythagoras theorem

BC ^2 = AB ^2 + AC ^2

= 15 ^2 + 20 ^2

= 225 + 400

= 625

BC = 25 cm

AB = 15 cm

AC = 20 cm