Question

The ratio of the base and the height of a triangle are 4:3. If the area of the triangle is 216 m2, find the length and height.

Answer 1

area of triangle is 1÷2b×h
let's take the ratios as 3x and 4x
1÷2×3x×4x=216
X= 61.7
3x = 185.1
4x = 246.8

Answer 2

The length of triangle is 30 m and height is 18 m.

Step-by-step explanation:

According to the question

The ratio of the base and the height of a triangle are 4 : 3.

The area of the triangle is $216\ m^{2}$.

we have to find the length and height.

Let the base and the height of a triangle are 4x and 3x.

We know that,

Area of triangle = $\frac{1}{2}\times b\times h$

$216 = \frac{1}{2}\times4x\times3x$

$216 = 2x\times3x$

$216 = 6x^2$

$\frac{216}{6} = x^2$

$36 = x^2$

$\sqrt{36} = x$

x = 6

base = 4 x 6 = 24  m

height = 3 x 6 = 18 m

Now, by Pythagorean Theorem

$a^{2}\ +\ b^{2} = c^{2}$ {where a = base, c = height and c = length}

$(24)^{2}\ +\ (18)^{2} = c^{2}$

$576\ +\ 324 = c^{2}$

$900 = c^{2}$

$\sqrt{900} = c$

c = 30 m

Therefore, the length of triangle is 30 m and height is 18 m.