Question

He height of a triangle is 4cm less than three time its base lenght. if the area is 80cm2, what are the lenght of the base and the height?
search instead for the hieght of a triangle is 4cm less than three time its base lenght. if the area is 80cm, what are the lenght of the base and the height?

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{\red{Solution}}}}}}$

$\Large{\underline{\mathfrak{\bf{\orange{Given}}}}}$

• height of a triangle is 4cm less than three time its base lenght
• Area of triangle = 80 cm²

$\Large{\underline{\mathfrak{\bf{\orange{Find}}}}}$

• Base & Height of triangle

$\Large{\underline{\underline{\mathfrak{\bf{\red{Explanation}}}}}}$

$\large{\underline{\mathfrak{\bf{\orange{Important\:Formula}}}}}$

$\boxed{\underline{\tt{\green{\:Area_{triangle}\:=\:\dfrac{Base \times Height}{2}}}}}$

So, Let

• Base = B
• Height = H

A/C to Question,

(Height of a triangle is 4cm less than three time its base length )

So, it Will be

➩ Height = 3*Base - 4

Or,

➩ H = 3B - 4 -----------(1)

Now,

➩ Area of triangle = 1/2 * Base * Height

Keep Value of Height , & Area of triangle

➩ 80 = 1/2 * B * ( 3*B - 4)

➩ 80 * 2 = 3*B² - 4*B

➩ 3B² - 4B - 160 = 0

➩3B² - 24B + 20B - 160 = 0

➩ 3B ( B - 8) + 20(B - 8) = 0

➩ (B - 8) (3B + 20) = 0

➩ ( B - 8) = 0. Or, ( 3B + 20) = 0

➩ B = 8. Or, B = -20/3

Here,Base( B ) = -20/3 is negative Value , So, this is negligible.

Now, Take B = 8 cm

Keel Value of B in equ(1)

➩ H = 3B - 4

➩ H = 3 * 8 - 4

➩ H = 24 - 4

➩ H = 20 cm

____________________

Base & Height of triangle

$\Large{\underline{\underline{\mathfrak{\bf{\red{Hence}}}}}}$

• Length of Base(B) = 8 cm
• Length of Height (H) = 20 cm

___________________

$\large{\underline{\mathfrak{\bf{\orange{Answer\:Verification}}}}}$

Keep Value of Base & Height in Formula

➩ Area of triangle = 80

➩ 1/2 * 8 * 20 = 80

➩ 4 * 20 = 80

➩ 80 = 80

L.H.S. = R.H.S.

That's Proved

We Can say that, our solution is absolutaly right .

___________________

Answer 2

★ The answer is refer to the attachment ★