Question

the base and height of a triangle are in the ratio 5:6. if the area of the triangle is 6000m², then find its base and height?​

Answer 1

Step-by-step explanation:

let the base=5x

and hieght=6x

area of triangle=6000 m^2

formula;

area of triangle=1/2 * height * base

6000=1/2 * 5x * 6x

6000*2= 30x^2

12000/30=x^2

400square root=x

x=20

height=6x=6*20=120m

base=5x=5*20=100m

Answer 2

Answer:-

Base and height of the triangle are 100 m and 120 m respectively.

Given:-

• The base and height of a triangle are in the ratio of 5:6.

• The area of triangle is 6000 $\sf{m^{2}}$.

To find:

The length of base and height.

Solution:

Let the constant be x.

According to the first condition.

=> Base=5x

=> Height=6x

$\boxed{\sf{Area \ of \ triangle=\frac{1}{2}\times \ Base\times \ Height}}$

According to the second condition.

$\sf{\frac{1}{2}\times5x\times6x=6000}$

$\sf{\therefore{15x^{2}=6000}}$

$\sf{\therefore{x^{2}=\frac{6000}{15}}}$

$\sf{\therefore{x^{2}=400}}$

On taking square root of both sides

=> x=20 or -20

But length can't be negative.

=> x=20

=> Base=5(20) =100 m

=> Height=6(20) =120 m

Base and height of the triangle are 100 m and 120 m respectively.