Question

5. The base and the height of a triangle are in
the ratio 4: 5. If the area of the triangle is
$40m {}^{2}$
; find its base and height.

Hint
$let \: \: \: base \: \: \: be \: \: 4xm \: \: and \: \: \: height \: \: \: \: be \: \: \: \: 5xm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: therefor \: \: \: 1 by \: \: 2 \times 4x \times 5x = 40$
answer is for the given question
8m and 10m



I have given the answers above the chapter is mensuration area of a Trapezium and a polygon please do in class 8th standard explain the method and solve it. only solve if you know otherwise don't solve thank you .​ don't give me any reply If you are going to write rubbish ​​

Answer 1

GIVEN:-

Let the Ratio be "x"

• $\rm{Base\:of\: triangle= 4x}$

• $\rm{Height\:of\:triangle=5x}$

• $\rm{Area\:of\: Triangle= 40m^2}$.

TO FIND:-

• Base and Height of the triangle.

FORMULAE USED

• ${\boxed{\rm{Area\:of\:\triangle=\dfrac{1}{2}\times{Base}\times{Height}}}}$

Now,

$\implies\rm{Area\:of\:triangle=\dfrac{1}{2}\times{Base}\times{Height}}$

$\implies\rm{40=\dfrac{1}{2}\times{4x}\times{5x}}$

$\implies\rm{40=\dfrac{20x^2}{2}}$

$\implies\rm{80=20x^2}$

$\implies\rm{x^2=\dfrac{\cancel{80}}{\cancel{20}}}$

$\implies\rm{x^2=\sqrt{4}}$.

$\implies\rm{x=2}$

Therefore,

$\implies\tt{Base=4x=8m}$

$\implies\tt{Height=5x=10}$

VERIFICATION

Area of triangle =1/2×base× Heigh

Area of triangle =1/2×8×10

Area of Triangle= 40m²

Answer 2

▪ Given -

First of all, Let's assume all ratio as x

• Base of Triangle = 4x
• Height of Triangle = 5x
• Area of Triangle = 40m^2

▪ To Find -

• Base & Height of Given Triangle

▪ Solution -

Here, Formula used is Area of Triangle -

• $area \: of \: triangle \: ∆ = \frac{1}{2} \times base \times height$

Placing Values according to given conditions -

$⟹40 = \frac{1}{2} \times 4</strong><strong>x</strong><strong> \times 5</strong><strong>x</strong><strong>$

$⟹40 = \frac{ {20x}^{2} }{2}$

$⟹80 = {2</strong><strong>0</strong><strong>x}^{2}$

$⟹ {x}^{2} = \frac{\cancel{80}}{\cancel{20}}4$

$⟹ {x}^{2} = \sqrt{14}$

$⟹x = 2$

Now, Let's find Base & height of triangle -

• Base =

$⟹base = 4x$

$⟹4 \times 2$

$⟹8$

• Height =

$⟹height = 5x$

$⟹5 \times 2$

$⟹10$

⛬ Base of triangle is 8cm & height is 10cm