Question

The area of a right triangle is 150 cm^2. If its attituds exceeds the base by 5 cm, calculate the perimeter of the triangle.

Right answer with steps will be marked brainlist. ​

Answer 1

Answer:

perimeter = 60 cm

Step-by-step explanation:

area of triangle = 1/2 × b × h = 150

let the base of triangle be x

height will be x + 5

$\frac{1}{2} \times x \times (x + 5) = 150 \\ {x}^{2} + 5x = 150 \times 2 \\ {x}^{2} + 5x = 300 \\ {x}^{2} + 5x - 300 = 0 \\ {x}^{2} + 20x - 15x - 300 = 0 \\ x(x + 20) - 15(x + 20) = 0 \\ (x + 20)(x - 15) = 0 \\ x + 20 = 0 \: \: \: \: \: x - 15 = 0 \\ x = - 20 \: \: \: \: \: \: \: x = 15$

we take the positive value of x

base = x = 15

height = x + 5 = 15 + 5 = 20

the third side is hypotenuse

${hyp}^{2} = {base}^{2} + {height}^{2} \\ = {20}^{2} + {15}^{2} \\ = 400 + 225 \\ = 625 \\ {hyp}^{2} = 625 \\ hyp = \sqrt{625} = 25$

perimeter of triangle is

15 + 20 + 25 = 60 cm

Answer 2

Step-by-step explanation:

Answer:

perimeter = 60 cm

Step-by-step explanation:

area of triangle = 1/2 × b × h = 150

let the base of triangle be x

height will be x + 5

\begin{gathered} \frac{1}{2} \times x \times (x + 5) = 150 \\ {x}^{2} + 5x = 150 \times 2 \\ {x}^{2} + 5x = 300 \\ {x}^{2} + 5x - 300 = 0 \\ {x}^{2} + 20x - 15x - 300 = 0 \\ x(x + 20) - 15(x + 20) = 0 \\ (x + 20)(x - 15) = 0 \\ x + 20 = 0 \: \: \: \: \: x - 15 = 0 \\ x = - 20 \: \: \: \: \: \: \: x = 15 \\ \end{gathered}

2

1

×x×(x+5)=150

x

2

+5x=150×2

x

2

+5x=300

x

2

+5x−300=0

x

2

+20x−15x−300=0

x(x+20)−15(x+20)=0

(x+20)(x−15)=0

x+20=0x−15=0

x=−20x=15

we take the positive value of x

base = x = 15

height = x + 5 = 15 + 5 = 20

the third side is hypotenuse

\begin{gathered} {hyp}^{2} = {base}^{2} + {height}^{2} \\ = {20}^{2} + {15}^{2} \\ = 400 + 225 \\ = 625 \\ {hyp}^{2} = 625 \\ hyp = \sqrt{625} = 25\end{gathered}

hyp

2

=base

2

+height

2

=20

2

+15

2

=400+225

=625

hyp

2

=625

hyp=

625

=25

perimeter of triangle is

15 + 20 + 25 = 60 cm