Question

The length of base and height of a triangle are in the ratio 4:5. If the area of the triangle is 40 sq. metre, find the length of its base and height.​

Answer 1

This is the problem's answer

Answer 2

Required Solution:

★ Height = 10m ; Base = 8m ★

Given:

• Length of base and height of a triangle are in the ratio 4:5.

• Area of triangle = 40 m²

To calculate:

• Length of its base and height.

Calculation:

Let the length of its base be 4x and height be 5x respectively.

Here, by forming a suitable equation we can find the value of length of its base and height.

We know that,

• Area of triangle = ½ × b × h

But, according to the question:

⇒ 40 = ½ × 4x × 5x

⇒ 40 = ½ × 20x²

⇒ 40 = 1 × 10x²

⇒ 40 = 10x²

⇒ $\sf { \dfrac{40}{10} }$ = x²

⇒ 4 = x²

⇒ √4 = x

⇒ 2 = x

Now, we got the value of x. As we assumed the length of its base be 4x and height be 5x, hence

→ Base = 4x

→ Base = ( 4 × 2 )m

→ Base = 8 m

Also,

→ Height = 5x

→ Height = ( 5 × 2 )m

→ Height = 10 m

Therefore, the length of its base and height is 8m and 10m.

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Verification:

Now, let us substitute the value in the LHS and RHS of the following area of the ∆ formula to check our answer.

• Area of triangle = ½ × b × h

⇒ 40 m² = ( ½ × 8 × 10 ) m²

⇒ 40 m² = ( 4 × 10 ) m²

⇒ 40 m² = 40 m²

⇒ LHS = RHS

Hence, verified!