Answer:

Given ,

base of a triangle = 4 times of its height

area of triangle = 50 cm^{2}cm

2

To find,

Length of its base

Solution,

Area of triangle = \frac{1}{2} bh

2

1

bh

Let the height of triangle be h

Then the base of a triangle = 4h

So , 50cm^{2} = \frac{1}{2}(4h)(h)50cm

2

=

2

1

(4h)(h)

50cm^{2} = 2h(h)50cm

2

=2h(h)

25 cm^{2} = h^{2}25cm

2

=h

2

Therefore , h = 5cm

Base = 4h = 4(5) = 20cm

Hence,the base of the triangle is 20 cm

Verified answer

Answer:

b = 5[tex]\sqrt{2}[/tex]; h = 10[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The area of a triangle = 1/2*b*h = 50[tex]cm^{2}[/tex]

Where b is base and h is height.

Here, they have given that h = 2b

If we substitute this in the first formula in the place of h, we get:

50 = 1/2*2b*b

50 = [tex]b^{2}[/tex]

[tex]\sqrt{50}[/tex] = b

[tex]\sqrt{25} \sqrt{2}[/tex] = b

5[tex]\sqrt{2}[/tex] = b

h = 2b

= 5[tex]\sqrt{2}[/tex]*2

= 10[tex]\sqrt{2}[/tex]

You can verify this by putting the values in the formula of the Area of a Triangle.

I hope this helps you :)