Question

In a triangle , if the length of the altitude is double the length of its base and the area is 400 sq cm, find the length of the base and altitude

Answer 1

this is the solution..

Answer 2

• Length of the base = 20 cm

• Length of the altitude = 40 cm

Given :

In a triangle , if the length of the altitude is double the length of its base and the area is 400 sq.cm

To find :

• Length of the base

• Length of the altitude

Solution :

Step 1 of 2 :

Form the equation to calculate length of the base and altitude

Let length of the base = b cm

Since the length of the altitude is double the length of its base

∴ Length of the altitude = 2b cm

Since area is 400 sq.cm

By the given condition

$\displaystyle \sf{ \frac{1}{2} \times Base \times Altitude = Area }$

$\displaystyle \sf{ \implies } \frac{1}{2} \times b \times 2b = 400$

Step 2 of 2 :

Calculate length of the base and altitude

$\displaystyle \sf \frac{1}{2} \times b \times 2b = 400$

$\displaystyle \sf{ \implies } {b}^{2} = 400$

$\displaystyle \sf{ \implies } {b}^{2} = {20}^{2}$

$\displaystyle \sf{ \implies }b = 20$

Length of the base = b = 20 cm

Length of the altitude

= 2b cm

= 2 × 20 cm

= 40 cm

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