Question

the length of base and height of a triangle are in the ratio 5 ratio 9 if the area of the triangle is 360 metre square find the length of its base and height​

Answer 1

Given

• Base and Height Ratio = 5:9
• Area = 360 m²

Explanation:

FORMULA

$\maltese \ {\pink{\large{\pmb{\boxed{\sf{ Area_{( \Delta )} = \dfrac{1}{2} \times Base \times Height }}}}}}$

Let the Base and Height of the Triangle be 5x and 9x

Now, We can find the lengths of its base and Height as:-

$\colon\implies{\sf{ Area_{( \Delta )} = \dfrac{1}{2} \times b \times h }} \\ \\ \\ \colon\implies{\sf{ 360 = \dfrac{1}{2} \times 5x \times 9x }} \\ \\ \\ \colon\implies{\sf{ 360 \times 2 = 5x \times 9x }} \\ \\ \\ \colon\implies{\sf{ \cancel{720} = \cancel{45} \ x^2 }} \\ \\ \\ \colon\implies{\sf{ x^2 = 16 }} \\ \\ \\ \colon\implies{\sf{ x = \sqrt{16} }} \\ \\ \colon\implies{\sf{ x = 4 }}$

So, We have to put value of x in base and Height of the triangle :-

$\maltese \ {\large{\pmb{\sf{ Base = 5x = 5 \times 4 = 20 \ metres}}}} \\ \\ \maltese \ {\large{\pmb{\sf{ Height = 9x =9 \times 4 = 36 \ metres}}}}$

Hence,

• The Base and Height of the Triangle are 20m and 36m Respectively.