Question

In a triangle the height is double the base and the area is 400 sqcm. Find the length of the base and height.​

Answer 1

Answer:

Area of a triangle=

2

1

×base×height

Let, base=x cm, then height=2x cm

So, 400cm

2

=1/2×(x)×(2x)

⟹x

2

=

2

400×2

=400cm

⟹x=20cm

So,

base=20cm;height=40cm

Answer 2

$\bf{Area \: of \: traingle = \dfrac{1}{2} \times Base \times Height}\\\\\\\rm{Let \: Base \: be \: b \: Height \: be \: 2b}\\\\\\\longrightarrow \sf{Area=\dfrac{1}{2} \times b \times 2b}\\\\\\\longrightarrow \sf{400 = \dfrac{1}{\not 2} \times b \times \not 2 b}\\\\\\\longrightarrow \sf{b^{2} = 400}\\\\\\\longrightarrow \sf{b = \sqrt{400} }\\\\\\\implies \sf{b = \pm 20}\\\\\\\sf{Base \: cannot \: be \: negative.}\\\\\\\therefore \bf \large \underline{Base = 20 \:cm}$

$Now \: let's \: find \: out \: the \: height\\\\\\\sf{Height = 2b}\\\\\implies \sf{Height = 2(20)}\\\\\implies \large{\boxed{\bf{Height = 40 \: cm}}}$