Question

The base and height of a triangle are in the ratio 4 : 5. If the area of a triangle is 2560 m², Find the length of base and height.​

Answer 1

Answer:

The base and height of a triangle are in the ratio 4 : 5. If the area of a triangle is 2560 m², then the length of the base is 64m and the height is 80m.​

Step-by-step explanation:

If the common multiple is x.

then the base of a triangle = 4x

And the height of a triangle = 5x

If the area of a triangle is 2560 m², then find the length of base and height.​

Formula:

Area of triangle = 1/2 × base × height

1/2 × 4x × 5x = 2560

$20x^2 = 5120\\x^2 = 5120/20\\x^2 = 256\\x = 16 m$

So, the base of a triangle = 4(16) = 64 m

And the height of a triangle = 5(16) =80 m

Answer 2

To find : the length of base and height of triangle

Given :  The base and height of a triangle are in the ratio $4 : 5$ and  area of a triangle is $2560$ m² .

Solution :  

• As per given data we know that the base and height of a triangle are in the ratio $4 : 5$ and area of a triangle is $2560$ m² .  
• Let , $4x$ and $5x$ be the base and height of triangle respectively .
• Area of triangle is given by ,

      Area of triangle =  $\frac{1}{2}\times base \times height$

• Substituting the value in above formula

      $2560= \frac{1}{2} \times 4x\times 5x$

      $2560 = 2x \times 5x \\ 2560 = 10 x^{2} \\x^{2} = \frac{2560}{10} \\ x^{2} = 256 \\ x= 16$

• Now , base = $4x = 4\times 16 = 64\ m$

                  height = $5x = 5\times 16 = 80\ m$

Hence , length of base and height of triangle are $64\ m$ and $80\ m$ respectively .